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1
CARUSO, SALVATORE. "Teoria della Funzione di Dissipazione: fondamenta matematiche per la fisica statistica di non equilibrio e per la teoria della risposta." Doctoral thesis, Università degli studi di Modena e Reggio Emilia, 2021. http://hdl.handle.net/11380/1245316.
Full textAbstract:
Le basi delle Leggi della Termodinamica stanno al centro della costruzione intellettuale della Fisica sin dalla loro prima formulazione alla fine del XIX secolo. A causa della loro centrale rilevanza, questi concetti suscitano ancora dibattiti molto accesi e alimentano feconde discussioni. Dato che questo è vero nel regno della fisica statistica dell'equilibrio - un corpus consolidato di concetti coerenti - la situazione è più instabile nella fisica statistica del non equilibrio, dove i dibattiti fondazionali sono ancora in corso. Questo stato di cose motiva lo studio dei fondamenti teorici e matematici della Fisica Statistica del Non Equilibrio. Oltre agli affascinanti aspetti scientifici, tali studi sono resi necessari da necessità tecnologiche: le bio- nano- tecnologie operano ad una scala in cui i confini tra macroscopico e microscopico sono sfumati; per di più in questi dispositivi il non equilibrio è la regola e non l'eccezione. Per tutti questi motivi, proponiamo la Teoria della Funzione di Dissipazione come base candidata per porre le basi teoriche e matematiche della Fisica Statistica del Non Equilibrio tramite una teoria della risposta non perturbativa.The foundations of the Laws of Thermodynamics stand in center of the intellectual building of Physics since their early formulation in late XIX century. Because of their central relevance, these concepts still spark flaming debates and propel profound discussions. Given that this is true in the realm of Equilibrium Statistical Physics -- an established corpus of coherent concepts -- the situation is even more volatile in Non Equilibrium Statistical Physics, where foundational debates are still going on. This state of things motivates the study of the theoretical and mathematical foundations of Non Equilibrium Statistical Physics. Besides the fascinating scientific aspects, such studies are made necessary by technological urgencies: bio- nano- technologies operate at a scale in which boundaries between macroscopic and microscopic are blurred, plus in these devices non equilibrium is the rule and not the exception. For all these reasons, we propose Dissipation Function Theory as a candidate base to lay the theoretical and mathematical foundations of Non Equilibrium Statistical Physics via a non perturbative response theory.
2
Melati, Alberto. "Renormalization of Wick polynomials for Boson fields in locally covariant AQFT." Doctoral thesis, Università degli studi di Trento, 2018. https://hdl.handle.net/11572/367938.
Full textAbstract:
The aim of this thesis is to study renormalization of Wick polynomials of quantum Boson fields in locally covariant algebraic quantum field theory in curved spacetime. Vector fields are described as sections of natural vector bundles over globally hyperbolic spacetimes and quantized in a locally covariant framework through the known functorial machinery in terms of local *-algebras. These quantized fields may be defined on spacetimes with given classical background fields, also sections of natural vector bundles: The most obvious one is the metric of the spacetime itself, but we encompass also the case of generic spacetime tensors as background fields. In our framework also physical quantities like the mass of the field or the coupling to the curvature are viewed as background fields. Wick powers of the quantized vector field are then axiomatically defined imposing in particular local covariance, scaling properties and smooth dependence on smooth perturbation of the background fields. A general classification theorem is established for finite renormalization terms (or counterterms) arising when comparing different solutions satisfying the defining axioms of Wick powers. The result is then specialized to the case of spacetime tensor fields. In particular, the case of a vector Klein-Gordon field and the case of a scalar field renormalized together with its derivatives are discussed as examples. In each case, a more precise statement about the structure of the counterterms is proved. The finite renormalization terms turn out to be finite-order polynomials tensorially and locally constructed with the backgrounds fields and their covariant derivatives whose coefficients are locally smooth functions of polynomial scalar invariants constructed from the so-called marginal subset of the background fields.
Our main technical tools are based on the Peetre-Slov\'ak theorem characterizing differential operators and on the classification of smooth invariants on representations of reductive Lie groups.
3
Guzzo, Marcelo Moraes [UNESP]. "Formulação diferencial em teorias de corda." Universidade Estadual Paulista (UNESP), 1987. http://hdl.handle.net/11449/132607.
Full textAbstract:
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4
Zanlungo, Francesco <1976>. "Microscopic dynamics of artificial life systems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/355/1/tesi_zanlungo.pdf.
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5
Zanlungo, Francesco <1976>. "Microscopic dynamics of artificial life systems." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/355/.
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6
Mura, Antonio <1978>. "Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2008. http://amsdottorato.unibo.it/846/1/Tesi_Mura_Antonio.pdf.
Full textAbstract:
This work provides a forward step in the study and comprehension of the relationships between
stochastic processes and a certain class of integral-partial differential equation, which can be used in
order to model anomalous diffusion and transport in statistical physics. In the first part, we brought
the reader through the fundamental notions of probability and stochastic processes, stochastic
integration and stochastic differential equations as well. In particular, within the study of H-sssi
processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process,
the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes.
The fGn, together with stationary FARIMA processes, is widely used in the modeling and
estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range
dependence, are often observed in nature especially in physics, meteorology, climatology, but also
in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real
data examples, providing statistical analysis and introducing parametric methods of estimation.
Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be
very appropriate for studying and modeling systems with long-memory properties. After having
introduced the basics concepts, we provided many examples and applications. For instance, we
investigated the relaxation equation with distributed order time-fractional derivatives, which
describes models characterized by a strong memory component and can be used to model relaxation
in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused
in the study of generalizations of the standard diffusion equation, by passing through the
preliminary study of the fractional forward drift equation. Such generalizations have been obtained
by using fractional integrals and derivatives of distributed orders. In order to find a connection
between the anomalous diffusion described by these equations and the long-range dependence, we
introduced and studied the generalized grey Brownian motion (ggBm), which is actually a
parametric class of H-sssi processes, which have indeed marginal probability density function
evolving in time according to a partial integro-differential equation of fractional type. The ggBm is
of course Non-Markovian. All around the work, we have remarked many times that, starting from a
master equation of a probability density function f(x,t), it is always possible to define an
equivalence class of stochastic processes with the same marginal density function f(x,t). All these
processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just
focused on a subclass made up of processes with stationary increments. The ggBm has been
defined canonically in the so called grey noise space. However, we have been able to provide a
characterization notwithstanding the underline probability space. We also pointed out that that the
generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular
it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and
analyzed a more general class of diffusion type equations related to certain non-Markovian
stochastic processes. We started from the forward drift equation, which have been made non-local
in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian
equation has been interpreted in a natural way as the evolution equation of the marginal density
function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t))
where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density
function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same
memory kernel K(t). We developed several applications and derived the exact solutions. Moreover,
we considered different stochastic models for the given equations, providing path simulations.
7
Mura, Antonio <1978>. "Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2008. http://amsdottorato.unibo.it/846/.
Full textAbstract:
This work provides a forward step in the study and comprehension of the relationships between
stochastic processes and a certain class of integral-partial differential equation, which can be used in
order to model anomalous diffusion and transport in statistical physics. In the first part, we brought
the reader through the fundamental notions of probability and stochastic processes, stochastic
integration and stochastic differential equations as well. In particular, within the study of H-sssi
processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process,
the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes.
The fGn, together with stationary FARIMA processes, is widely used in the modeling and
estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range
dependence, are often observed in nature especially in physics, meteorology, climatology, but also
in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real
data examples, providing statistical analysis and introducing parametric methods of estimation.
Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be
very appropriate for studying and modeling systems with long-memory properties. After having
introduced the basics concepts, we provided many examples and applications. For instance, we
investigated the relaxation equation with distributed order time-fractional derivatives, which
describes models characterized by a strong memory component and can be used to model relaxation
in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused
in the study of generalizations of the standard diffusion equation, by passing through the
preliminary study of the fractional forward drift equation. Such generalizations have been obtained
by using fractional integrals and derivatives of distributed orders. In order to find a connection
between the anomalous diffusion described by these equations and the long-range dependence, we
introduced and studied the generalized grey Brownian motion (ggBm), which is actually a
parametric class of H-sssi processes, which have indeed marginal probability density function
evolving in time according to a partial integro-differential equation of fractional type. The ggBm is
of course Non-Markovian. All around the work, we have remarked many times that, starting from a
master equation of a probability density function f(x,t), it is always possible to define an
equivalence class of stochastic processes with the same marginal density function f(x,t). All these
processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just
focused on a subclass made up of processes with stationary increments. The ggBm has been
defined canonically in the so called grey noise space. However, we have been able to provide a
characterization notwithstanding the underline probability space. We also pointed out that that the
generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular
it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and
analyzed a more general class of diffusion type equations related to certain non-Markovian
stochastic processes. We started from the forward drift equation, which have been made non-local
in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian
equation has been interpreted in a natural way as the evolution equation of the marginal density
function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t))
where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density
function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same
memory kernel K(t). We developed several applications and derived the exact solutions. Moreover,
we considered different stochastic models for the given equations, providing path simulations.
8
Melati, Alberto. "Renormalization of Wick polynomials for Boson fields in locally covariant AQFT." Doctoral thesis, University of Trento, 2018. http://eprints-phd.biblio.unitn.it/2836/1/PhD_Melati.pdf.
Full textAbstract:
The aim of this thesis is to study renormalization of Wick polynomials of quantum Boson fields in locally covariant algebraic quantum field theory in curved spacetime. Vector fields are described as sections of natural vector bundles over globally hyperbolic spacetimes and quantized in a locally covariant framework through the known functorial machinery in terms of local *-algebras. These quantized fields may be defined on spacetimes with given classical background fields, also sections of natural vector bundles: The most obvious one is the metric of the spacetime itself, but we encompass also the case of generic spacetime tensors as background fields. In our framework also physical quantities like the mass of the field or the coupling to the curvature are viewed as background fields. Wick powers of the quantized vector field are then axiomatically defined imposing in particular local covariance, scaling properties and smooth dependence on smooth perturbation of the background fields. A general classification theorem is established for finite renormalization terms (or counterterms) arising when comparing different solutions satisfying the defining axioms of Wick powers. The result is then specialized to the case of spacetime tensor fields. In particular, the case of a vector Klein-Gordon field and the case of a scalar field renormalized together with its derivatives are discussed as examples. In each case, a more precise statement about the structure of the counterterms is proved. The finite renormalization terms turn out to be finite-order polynomials tensorially and locally constructed with the backgrounds fields and their covariant derivatives whose coefficients are locally smooth functions of polynomial scalar invariants constructed from the so-called marginal subset of the background fields.
Our main technical tools are based on the Peetre-Slov\'ak theorem characterizing differential operators and on the classification of smooth invariants on representations of reductive Lie groups.
9
Kraenkel, Roberto André [UNESP]. "Cálculo variacional exterior." Universidade Estadual Paulista (UNESP), 1988. http://hdl.handle.net/11449/132808.
Full textAbstract:
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10
FILACI, MANUELE. "Neutrino Mass Models: From Type III See-saw to Non-Commutative Geometry." Doctoral thesis, Università degli studi di Genova, 2021. http://hdl.handle.net/11567/1045600.
Full textAbstract:
Today we know that neutrinos are massive, but we ignore both the origin of their masses and the reason why those masses are so tiny. A natural mechanism that can explain the smallness of neutrino masses is the See-saw Mechanism, that in this work is studied in its Type III variant. However, even in the scope of the See-saw Mechanism, the origin of the huge neutrino Majorana mass (which is a fundamental prerequisite for any see-saw model) remains to be explained. A possible explanation can be found in Twisted Non-Commutative Geometry (NCG): for particular twists of the so-called Connes Model (which is the NCG formulation of the Standard Model) a new scalar field appears naturally, whose vacuum expectation value generates a Majorana mass for the neutrinos, and the order of magnitude of said v.e.v. is precisely the natural scale of the Majorana mass of See-saw Mechanisms (10^15 GeV). In this work, three different twists of the Connes Model are studied, paying particular attention to the new boson field content, their gauge transformations, as well as the fermionic actions of each model.
11
Fleury, Thiago Simonetti [UNESP]. "Harmonic superspace from the Ad'S IND. 5' × 'S POT. 5' pure spinor formalism." Universidade Estadual Paulista (UNESP), 2013. http://hdl.handle.net/11449/108876.
Full textAbstract:
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000773092.pdf: 628332 bytes, checksum: eb30fdb970ce8b80e0cf4467a8bb5c64 (MD5)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
A conjectura de Maldacena ou (AdS/CFT) desde a sua formulação é um dos tópicos em física de altas energias mais estudados. Uma das versões da conjectura é a dualidade entre a teoria de supercordas do tipo IIB em um background Ad'S IND. 5' × 'S POT. 5' suportado por um ?uxo Ramond-Ramond e a teoria deN = 4 super-YangMills em quatro dimensões. Embora a ação para supercordas neste background seja conhecida tanto no formalismo de Green-Schwarz como no formalismo de espinores puros, a construção explícita dos operadores de vértice da teoria em termos de supercampos é um problema em aberto. Nesta tese, os operadores de vértice do formalismo de espinores puros correspondentes aos estados de supergravidade são construídos próximos a fronteira de AdS. A conjectura prevê que todo estado na camada de massa da supercorda é dual a um operador invariante de gauge de N = 4 d = 4 super-Yang-Mills, em particular, os estados de supergravidade são duais a operadores Half-BPS. Os operadores Half-BPS e seus duais podem ser descritos como supercampos em um superespaço harmônico. Os resultados obtidos para os operadores de vértice são descritos em função desses supercampos duais de acordo com o previsto pela conjectura
The Maldacena’s conjecture or (AdS/CFT) has been one of the most studied topics in high energy physics since its formulation. One of the versions of the conjecture is the duality between the theory of type IIB superstrings in the background Ad'S IND. 5' × 'S POT. 5' supported by a Ramond-Ramond ?ux and the theory of N = 4 superYang-Mills in four dimensions. Although the action for the superstrings in this background is known both in the Green-Schwarz and in the pure spinor formalisms, an explicit super?eld construction of the vertex operators of the theory is an open problem. In this thesis, using the pure spinor formalism, we explicitly construct the vertex operators corresponding to supergravity states close to the boundary ofAdS. The conjecture predicts that every on-shell superstring state is dual to a gaugeinvariant operator of N = 4d = 4 super-Yang-Mills, in particular, the supergravity states are dual to Half-BPS operators. It is possible to describe all the Half-BPS operators and their duals as super?elds in harmonic superspace. The results for the vertex operators are described in terms of these dual super?elds in agreement with the prediction of the conjecture
FAPESP: 09/50775-3
12
Vaccari, Alessandro. "Modeling the interaction of light with photonic structures by direct numerical solution of Maxwell's equations." Doctoral thesis, University of Trento, 2015. http://eprints-phd.biblio.unitn.it/1415/1/Tesi_dottorato_Vaccari_Alessandro.pdf.
Full textAbstract:
The present work analyzes and describes a method for the direct numerical solution of the Maxwell's equations of classical electromagnetism. This is the FDTD (Finite-Difference Time-Domain) method, along with its implementation in an "in-house" computing code for large parallelized simulations. Both are then applied to the modelization of photonic and plasmonic structures interacting with light. These systems are often too complex, either geometrically and materially, in order to be mathematically tractable and an exact analytic solution in closed form, or as a series expansion, cannot be obtained. The only way to gain insight on their physical behavior is thus to try to get a numerical approximated, although convergent, solution. This is a current trend in modern physics because, apart from perturbative methods and asymptotic analysis, which represent, where applicable, the typical instruments to deal with complex physico-mathematical problems, the only general way to approach such problems is based on the direct approximated numerical solution of the governing equations. Today this last choice is made possible through the enormous and widespread computational capabilities offered by modern computers, in particular High Performance Computing (HPC) done using parallel machines with a large number of CPUs working concurrently. Computer simulations are now a sort of virtual laboratories, which can be rapidly and costless setup to investigate various physical phenomena. Thus computational physics has become a sort of third way between the experimental and theoretical branches. The plasmonics application of the present work concerns the scattering and absorption analysis from single and arrayed metal nanoparticles, when surface plasmons are excited by an impinging beam of light, to study the radiation distribution inside a silicon substrate behind them. This has potential applications in improving the eciency of photovoltaic cells.
The photonics application of the present work concerns the analysis of the optical reflectance and transmittance properties of an opal crystal. This is a regular and ordered lattice of macroscopic particles which can stops light propagation in certain wavelenght bands, and whose study has potential applications in the realization of low threshold laser, optical waveguides and sensors. For these latters, in fact, the crystal response is tuned to its structure parameters and symmetry and varies by varying them. The present work about the FDTD method represents an enhacement of a previous one made for my MSc Degree Thesis in Physics, which has also now geared toward the visible and neighboring parts of the electromagnetic spectrum. It is organized in the following fashion. Part I provides an exposition of the basic concepts of electromagnetism which constitute the minimum, although partial, theoretical background useful to formulate the physics of the systems here analyzed or to be analyzed in possible further developments of the work. It summarizes Maxwell's equations in matter and the time domain description of temporally dispersive media. It addresses also the plane wave representation of an electromagnetic field distribution, mainly the far field one. The Kirchhoff formula is described and deduced, to calculate the angular radiation distribution around a scatterer. Gaussian beams in the paraxial approximation are also slightly treated, along with their focalization by means of an approximated diraction formula useful for their numericall FDTD representation. Finally, a thorough description of planarly multilayered media is included, which can play an important ancillary role in the homogenization procedure of a photonic crystal, as described in Part III, but also in other optical analyses. Part II properly concerns the FDTD numerical method description and implementation. Various aspects of the method are treated which globally contribute to a working and robust overall algorithm. Particular emphasis is given to those arguments representing an enhancement of previous work.These are: the analysis from existing literature of a new class of absorbing boundary conditions, the so called Convolutional-Perfectly Matched Layer,
and their implementation; the analysis from existing literature and implementation of the Auxiliary Differential Equation Method for the inclusion of frequency dependent electric permittivity media, according to various and
general polarization models; the description and implementation of a "plane wave injector" for representing impinging beam of lights propagating in an arbitrary direction, and which can be used to represent, by superposition, focalized beams; the parallelization of the FDTD numerical method by means of the Message Passing Interface (MPI) which, by using the here proposed,
suitable, user dened MPI data structures, results in a robust and scalable code, running on massively parallel High Performance Computing Machines like the IBM/BlueGeneQ with a core number of order 2X10^5. Finally, Part III gives the details of the specific plasmonics and photonics applications made with the "in-house" developed FDTD algorithm, to demonstrate its effectiveness. After Chapter 10, devoted to the validation of the FDTD code implementation against a known solution, Chapter 11 is about plasmonics, with the analytical and numerical study of single and arrayed metal nanoparticles of different shapes and sizes, when surface plasmon are excited on them by a light beam. The presence of a passivating embedding silica layer and a silicon substrate are also included. The next Chapter 12 is about the FDTD modelization of a face-cubic centered (FCC) opal photonic crystal sample, with a comparison between the numerical and experimental transmittance/reflectance behavior. An homogenization procedure is suggested of the lattice discontinuous crystal structure, by means of an averaging procedure and a planarly multilayered media analysis, through which better understand the reflecting characteristic of the crystal sample.
Finally, a procedure for the numerical reconstruction of the crystal dispersion banded omega-k curve inside the first Brillouin zone is proposed. Three Appendices providing details about specific arguments dealt with during the exposition conclude the work.
13
Tesei, Edoardo. "Teoria della Relatività e Geometrie dell'Universo." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23231/.
Full textAbstract:
La seguente tesi vuole evidenziare il profondo legame tra la fisica e la geometria presentando la Teoria della Relatività di Einstein e rimarcandone la natura geometrica. Nella prima parte si forniscono gli strumenti matematici necessari alla modelizzazione di uno spazio curvo, più generale del classico spazio piatto Euclideo, e si descrivono oggetti dell'algebra multilineare - i tensori - utili a formalizzare l'invarianza delle leggi fisiche per diversi osservatori. Si rimarcherà come le quantità invarianti abbiano un ruolo quasi secondario in una teoria fisica rispetto alle relazioni covarianti e si estenderà la nozione di differenziazione nota per i campi vettoriali a campi tensoriali definiti su generici spazi curvi. Nella seconda parte si presenta la Relatività Ristretta, non nel modo in cui fu diffusa originariamente da Einstein, bensì alla maniera di Minkowski, che è stato il primo a darne una profonda interpretazione geometrica, gettando le basi per la sua futura generalizzazione. Tramite il formalismo tensoriale, si vede come la Relatività Ristretta costituisca solo un'approssimazione locale di una geometria globalmente più complessa, che risulta distendersi su uno spazio-tempo quadrimensionale curvo. Nella terza parte si costruisce la Relatività Generale, teoria geometrica della gravità, e si deducono le equazioni differenziali per il campo gravitazionale, le cui soluzioni costituiscono una possibile metrica dello spazio-tempo nonché del campo gravitazionale stesso. Si presenta, quindi, la soluzione di Robertson-Walker per un modello cosmologico di universo omogeneo e isotropo che risulta essere dinamico, non statico, e, ancora mediante argomentazioni tensoriali, si conclude che la sua curvatura deve necessariamene essere costante. Da qui si deducono le possibili geometrie dell'universo e mediante le equazioni di Friedmann si accenna allo studio dell'evoluzione temporale di uno spazio-tempo piatto, sferico o iperbolico.
14
De, Palma Giacomo. "Gaussian optimizers and other topics in quantum information." Doctoral thesis, Scuola Normale Superiore, 2016. http://hdl.handle.net/11384/86203.
Full textAbstract:
Gaussian input states have long been conjectured to minimize the output von Neumann entropy of quantum Gaussian channels for fixed input entropy. We prove the quantum Entropy Power Inequality, that provides an extremely tight lower bound to this minimum output entropy, but is not saturated by Gaussian states, hence it is not sufficient to prove their optimality. Passive states are diagonal in the energy eigenbasis and their eigenvalues decrease as the energy increases. We prove that for any one-mode Gaussian channel, the output generated by a passive state majorizes the output generated by any state with the same spectrum, hence it has a lower entropy. Then, the minimizers of the output entropy of a Gaussian channel for fixed input entropy are passive states. We exploit this result to prove that Gaussian states minimize the output entropy of the one-mode attenuator for fixed input entropy. This result opens the way to the multimode generalization, that permits to determine both the classical capacity region of the Gaussian quantum degraded broadcast channel and the triple trade-off region of the quantum attenuator. Still in the context of Gaussian quantum information, we determine the classical information capacity of a quantum Gaussian channel with memory effects. Moreover, we prove that any one-mode linear trace-preserving not necessarily positive map preserving the set of Gaussian states is a quantum Gaussian channel composed with the phase-space dilatation. These maps are tests for certifying that a given quantum state does not belong to the convex hull of Gaussian states. Our result proves that phase-space dilatations are the only test of this kind. In the context of quantum statistical mechanics, we prove that requiring thermalization of a quantum system in contact with a heat bath for any initial uncorrelated state with a well-defined temperature implies the Eigenstate Thermalization Hypothesis for the system-bath Hamiltonian. Then, the ETH constitutes the unique criterion to decide whether a given system-bath dynamics always leads to thermalization. In the context of relativistic quantum information, we prove that any measurement able to distinguish a coherent superposition of two wavepackets of a massive or charged particle from the corresponding incoherent statistical mixture must require a minimum time. This bound provides an indirect evidence for the existence of quantum gravitational radiation and for the necessity of quantizing gravity.
15
Benedetti, Alessandro. "Introduzione alla Teoria Quantistica dei Campi: Spazi di Fock e il modello." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18314/.
Full textAbstract:
La QFT è una teoria nata in ambito fisico per risolvere alcuni problematiche della teoria quantistica delle particelle, dando risultati sorprendenti. Nasce come teoria effettiva a cui fu successivamente necessario dare un rigore matematico. In generale le strutture matematiche teorizzate non risultano adeguate a modellare un ampio spettro di sistemi fisici. Esistono tuttavia dei modelli “giocattolo” perfettamente coerenti per i quali sono stati creati strumenti molto interessanti ed efficaci, come ad esempio gli spazi di Fock.
In questa tesi oltre a una presentazione dettagliata degli spazi di Fock verrà descritto un esempio non banale della loro applicazione: il modello interattivo e ristretto ad una
sola dimensione spaziale
16
Rosa, Valentina. "Forme differenziali e applicazioni alla fisica e biologia molecolare." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23116/.
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Questa tesi tratta delle k-forme differenziali come utili strumenti in ambito fisico e biochimico. Dopo averle definite, si osserveranno alcune proprietà e operatori importanti, quali il pullback, la derivazione esterna e l'operatore * di Hodge. Sulla base di queste conoscenze verranno riscritte le equazioni di Maxwell in forma più compatta attraverso le k-forme. In seguito verrà introdotto il concetto di "linking number" mediante la definizione di grado di una funzione. Grazie alla teoria dei nodi sarà possibile studiare questo invariante topologico nel contesto del DNA e delle proteine: non esiste un metodo sperimentale per osservare direttamente la dinamica dell'azione enzimatica, ma grazie agli studi sui cambiamenti nella geometria del DNA e delle proteine è ora possibile dedurre i meccanismi degli enzimi e prevenire alcune patologie dovute a folding errati.
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Botari, Tiago [UNESP]. "Aceleração de Fermi em bilhares com fronteiras dependentes do tempo descritas por osciladores não lineares: caso conservativo e dissipativo." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/91917.
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botari_t_me_rcla.pdf: 1184185 bytes, checksum: 8ca4a5b0e289b60ba95cbdc707d3ebe4 (MD5)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
Neste trabalho estudamos dois bilhares com fronteira móvel cuja perturbação temporal é dada por um oscilador van der Pol. Estudamos um bilhar unidimensional e outro bidimensional na qual uma ou mais partículas clássicas de massa m não interagentes são confnadas ao interior da fronteira que defne o bilhar. Investigando algumas propriedades dinâmicas e estatísticas da partícula em função do parâmetro X que controla o termo não linear e o parâmetro y0 que controla a amplitude do oscilador de van der Pol. O bilhar unidimensional consiste em duas paredes rígidas, em que uma delas é móvel centrada na origem regida pelo oscilador de van der Pol e a outra xa em L. Descrevemos todos os procedimentos para construção do mapeamento que fornece a dinâmica da partícula, assim como as equações necessárias que defnem o movimento da parede móvel. O espaço de fases, o expoente de Lyapunov e a velocidade média são obtidos para diferentes valores de parâmetros de controle. Para o caso em que massa da partícula (mp) é muito menor que a massa da parede móvel (mw), m = mp=mw ' 0, podemos dividir o regime dinâmico em função do parâmetro c em dois tipos: (i) que recupera os resultados do modelo Fermi- Ulam; e (ii) no qual é observado um regime de crescimento da velocidade média nal. Para o caso em que m 6= 0, as colisões da partícula com a parede móvel perturbam o movimento da parede móvel e o sistema se torna dissipativo. Neste caso a dinâmica da partícula tende a pontos xos de forma assintótica passando por um transiente inicial. Para este caso construímos a bacia de atração e a frequência do número de períodos de um conjunto de condições iniciais. Para o bilhar bidimensional, construímos um modelo em que a fronteira é do tipo ovoide, analisamos o caso estático e o móvel regida pelo oscilador de van der Pol...
Some dynamical properties for an ensemble of non-interacting particles con ned in a billiard with a time-dependent boundary are studied. The boundary is given by van der Pol oscillator and two cases are considered namely: (i) one-dimensional and (ii) twodimensional dynamics. For the one-dimensional case, we considered the dynamics of classical particle of mass m con ned to bounce between two rigid walls. One of them is xed at a distance L from the average position of the rst that uctuates according to a van der Pol oscillator. We consider the case where the mass of the particle is su ciently small as compared to the mass of the moving wall. Then we investigate some properties of the phase space including the average velocity of the particle. Our results reveal a scaling invariance for the nal average velocity, i.e., when n!¥. We discuss also the case when the mass of the particle is a fraction of the mass of the moving wall therefore showing the system now shows features of dissipative model. This is characterized speci cally by the presence of attractors in the phase space. For the two-dimensional case, we considered the dynamics of a classical particle of mass m where the particle is con ned to bounce inside a billiard whose boundary is of ellipticaloval like shape. First we analyze the static case. Second we consider the case where the boundary moves according to a van der Pol oscillator. We discuss the model in a similar way as made for the 1-D case including very small mass of the particle (m = 0) and m 6= 0. Dynamical properties for the particle were obtained like the behavior of the average velocity therefore demonstrating that unlimited energy gain is in course, as predicted by the LRA conjecture For the case of... (Complete abstract click electronic access below)
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Teodoro, Marcio Daldin. "Efeito Aharonov-Bohm em partículas neutras." Universidade Federal de São Carlos, 2011. https://repositorio.ufscar.br/handle/ufscar/4930.
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Previous issue date: 2011-03-14Universidade Federal de Sao Carlos
In classical Physics, the motion of an electrically charged particle is affected only by the presence of a magnetic field if the particle enters a region of space in which the field is present. Meanwhile, in quantum Physics, a charged carrier can be affected by the electromagnetic vector potential ~A, even in regions where the magnetic field ~B is not present. This surprising contrast between classical and quantum Physics has been experimentally proven in several beautiful experiments in semiconducting, metallic and superconducting material systems, and has been called Aharonov-Bohm effect. More recently, however, several theoretical works have discussed the plausible existence of this effect even for neutral particles! In this PhD Thesis project it is shown the first clear experimental observation of the Aharonov-Bohm effect in neutral excitons in InAs quantum rings. Signatures of this effect appear as oscillations in the intensity of the photoluminescence emission bands with increasing magnetic fields and also depending on the dimensions of the quantum rings. These oscillations are affected by the uniaxial strain field due to the piezoelectricity of the asymmetric InAs rings, as revealed by the atomic force microscopy, transmission electron microscopy images and X-Ray Diffraction measurements using synchrotron light. A theoretical model that describes the behavior of the excitonic interference pattern and its modulation with temperature and uniaxial electric fields has been used for the interpretation of the experimental data. The detection of AB oscillations mediated by electron-hole pair correlation is a fundamental quantum mechanical effect that will trigger further studies in this area of fundamental physics as well as technological applications.
Em Física clássica, o movimento de uma partícula carregada só é afetado pela presença de um campo magnético se a partícula entrar em uma região do espaço na qual o campo está presente. Ao mesmo tempo, em Física quântica, a partícula contendo carga elétrica pode ser afetada por um potencial eletromagnético ~ A, mesmo em regiões onde o campo magnético ~B é zero. Esse contraste surpreendente entre Física clássica e Física quântica tem sido provado em interessantes experimentos em materiais semicondutores, metais e supercondutores, e tendo sido denominado efeito Aharonov-Bohm. Mais recentemente, entretanto, muitos trabalhos teóricos têm discutido a plausibilidade da existência desse efeito mesmo para partículas neutras! Nessa tese de Doutorado será demonstrado pela primeira vez a observação experimental do efeito Aharonov-Bohm em éxcitons neutros contidos em anéis quânticos de InAs. Assinaturas desse efeito aparecem como oscilações na intensidade integrada das bandas de emissão em experimentos de fotoluminescência com o aumento do campo magnético e dependem também das dimensões dos anéis. Essas oscilações são afetadas pelos campos de compressão/expansão uniaxial devido a piezoeletricidade provinda da assimetria dos anéis, como revelado pelas imagens de microscopia de força atômica, microscopia eletrônica de transmissão e difração de raios-X utilizando luz síncrotron. Um modelo teórico que descreve o comportamento no padrão de interferência excitônico e sua modulação com a temperatura e campos elétricos uniaxiais foi usado para a interpretação dos resultados experimentais. A detecção das oscilações Aharonov-Bohm mediada pela correlação do par elétron-buraco é um efeito fundamental de mecânica quântica e os estudos mostrados aqui poderão não só instigar outras investigações em Física fundamental assim como em aplicações tecnológicas.
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França, Guilherme Starvaggi [UNESP]. "Estrutura algébrica de hierarquias integráveis e problemas de valor de contorno." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/102495.
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franca_gs_dr_ift.pdf: 535273 bytes, checksum: edf04248b447d90dd177d59543bbdce5 (MD5)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Nesta tese abordamos dois problemas. O primeiro trata-se do problema de condição de contorno para hierarquias integráveis. Através do método de dressing, que foi utilizado com êxito para construir soluções do tipo sóliton com condição de contorno nula, propomos uma abordagem geral para resolver o problema com condição de contorno não nula, onde o vácuo possui uma configuração de campos não trivial. Aplicamos então este método, para as hierarquias mKdV e AKNS com condição de contorno constante. Introduzimos operadores de vértice que incorporam a condição de contorno do problema, generalizando os operadores de vértice utilizados anteriormente. Quando o vácuo tende a zero, recuperamos os resultados conhecidos com condição de contorno nula. Soluções interessantes como dark sólitons, table-top sólitons, kinks, breathers e wobbles são obtidas para todas as equações da hierarquia mKdV. Introduzimos também, uma deformação integrável da hierarquia mKdV que contém a equaçãoo de Gardner. Soluções com condição de contorno nula desta hierarquia estão relacionadas com soluções de vácuo não trivial da hierarquia mKdV. O segundo problema consiste numa generalização da construção Lie algébrica da equação curvatura nula. A construção usual foi motivada pela estrutura dos modelos de Toda afim e é capaz de gerar as hierarquias mKdV/sinh-Gordon e AKNS/Lund-Regge. Propomos uma generalização que contém, além destas, outras hierarquias integráveis como as hierarquias de Wadati-Konno-Ichikawa (WKI) e Kaup-Newell (KN). Estas hierarquias contém modelos interessantes e alguns deles não foram suficientemente estudados, especialmente os de fluxo negativo. Mostramos que equações...
In this thesis we approach two distinct problems. The first one deals with boundary value problems for integrable hierarchies. Through the dressing method, which was successfully employed in the construction of vanishing boundary soliton solutions, we propose an algebraic approach to solve the nonvanishing boundary value problem where the vacuum has a nontrivial field configuration. We apply the proposed method to the mKdV and AKNS hierarchies with a constant boundary value. We introduce vertex operators that takes into account the boundary condition, generalizing previous known vertex operators. When the vacuum tends to zero, we recover previous known results with vanishing boundary condition. Interesting solutions arises like dark solitons, table-top solitons, kinks, breathers and wobbles for the whole mKdV hierarchy. We also introduce an integrable deformation of the mKdV hierarchy containing the Gardner equation. Solutions of this deformed hierarchy are related with nontrivial vacuum solutions of the mKdV hierarchy. The second problem consists in a generalization of the Lie algebraic structure of the zero curvature equation. The usual construction was motivated by affine Toda field theories and can generate the mKdV/sinh-Gordon and AKNS/Lund-Regge hierarchies. We propose a new construction that contains, besides them, other integrable hierarchies like the Wadati-Konno-Ichikawa (WKI) and Kaup-Newell (KN). We show that interesting models like the short-pulse equation recently proposed by Schafer-Wayne and the bosonic Thirring model, arise naturally from this construction. Moreover, this construction embraces a larger class of models into a systematic algebraic... (Complete abstract click electronic access below)
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Scherer, Caio Sarmento. "Modelos cinéticos da equação linearizada de Boltzmann e um problema de transferência de calor em microescala." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2005. http://hdl.handle.net/10183/4464.
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Neste trabalho, um problema de transferência de calor da dinâmica de gases rarefeitos, causado pela diferença de temperaturas nas superfícies de um canal, é abordado. O problema é formulado através dos modelos cinéticos BGK, S e Gross-Jackson da equação linearizada de Boltzmann e resolvido, de forma unificada, pelo método analítico de ordenadas discretas (método ADO). Resultados numéricos para as perturbações de densidade e temperatura e também para o fluxo de calor são apresentados e comparados, mostrando que não se pode dizer que algum dos três modelos seja uma melhor aproximação da solução aos resultados da equação linearizada de Boltzmann.In this work, a heat transfer problem in the rarefied gas dynamics field, in a plane channel, is studied. In particular, the flow is induced by different temperatures at the wall surfaces. The formulation of the problem is based in an ”unified” kinetic equation which includes the BGK model, the S-model and the Gross-Jackson model of the linearized Boltzmann equation. An analytical version of the discrete-ordinates method (the ADO method) is used to develop the solution and to evaluate the density, temperature and heat-flow profiles. Numerical results are presented and used to establish comparisons with the linearized Boltzmann equation results. It is shown that, for an analysis based in all cases, it is not possible to say that one of the models is a better approximation of the solution of the linearized Boltzmann equation.
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Oliveira, Ana Carolina de [UNESP]. "Quatérnios, operadores de Fueter e relações quaterniônicas transcendentais." Universidade Estadual Paulista (UNESP), 2006. http://hdl.handle.net/11449/94269.
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oliveira_ac_me_sjrp.pdf: 346640 bytes, checksum: dfe236f71e5ef2c050420d64d2c48a70 (MD5)O objetivo deste trabalho é estabelecer similaridades entre os complexos e os hipercomplexos, motivados em explorar idéias de Murnaghan, que introduziu, pela primeira vez, em uma apresentação elementar, a teoria dos quatérnios baseados no teorema de Moivre. É mostrada em detalhes uma analogia da relação complexa clássica de Moivre para quatérnios, e em brevidade para octônios generalizados, e apresenta-se as conexões com os operadores da teoria de Fueter e as funções transcendentais. A extensão do teorema de Moivre é estudada para quatérnios em definindo-se uma função exponencial quaterniônica.
In this work we establish similarities between the complex and the hipercomplex numbers, motivated in exploring ideas of Murnaghan, that introduced, for the first time, in an elementary presentation, the theory of the quaternions based on the theorem of Moivre. We show an analogy of the classic complex relation of Moivre for quaternions, and briefly discuss generalized octonions, as well as to present connections to operators of the theory of Fueter and transcendental functions. We consider them to study the extension of the theorem of Moivre for quaternions, in defining a exponential function on the quaternions.
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Brighi, Massimo <1954>. "Implicazioni teoriche e sperimentali della sincronizzazione assoluta nella teoria della relatività speciale." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amsdottorato.unibo.it/6232/1/Brighi_Massimo_tesi.pdf.
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Sono indagate le implicazioni teoriche e sperimentali derivanti dall'assunzione, nella teoria della relatività speciale, di un criterio di sincronizzazione (detta assoluta) diverso da quello standard.
La scelta della sincronizzazione assoluta è giustificata da alcune considerazioni di carattere epistemologico sullo status di fenomeni quali la contrazione delle lunghezze e la dilatazione del tempo. Oltre che a fornire una diversa interpretazione, la sincronizzazione assoluta rappresenta una estensione del campo di applicazione della relatività speciale in quanto può essere attuata anche in sistemi di riferimento accelerati. Questa estensione consente di trattare in maniera unitaria i fenomeni sia in sistemi di riferimento inerziali che accelerati.
L'introduzione della sincronizzazione assoluta implica una modifica delle trasformazioni di Lorentz. Una caratteristica di queste nuove trasformazioni (dette inerziali) è che la trasformazione del tempo è indipendente dalle coordinate spaziali.
Le trasformazioni inerziali sono ottenute nel caso generale tra due sistemi di riferimento aventi velocità (assolute) u1 e u2 comunque orientate. Viene mostrato che le trasformazioni inerziali possono formare un gruppo pur di prendere in considerazione anche riferimenti non fisicamente realizzabili perché superluminali.
È analizzato il moto rigido secondo Born di un corpo esteso considerando la sincronizzazione assoluta.
Sulla base delle trasformazioni inerziali si derivano le trasformazioni per i campi elettromagnetici e le equazioni di questi campi (che sostituiscono le equazioni di Maxwell). Si mostra che queste equazioni contengono soluzioni in assenza di cariche che si propagano nello spazio come onde generalmente anisotrope in accordo con quanto previsto dalle trasformazioni inerziali. L'applicazione di questa teoria elettromagnetica a sistemi accelerati mostra l'esistenza di fenomeni mai osservati che, pur non essendo in contraddizione con la relatività standard, ne forzano l'interpretazione. Viene proposto e descritto un esperimento in cui uno di questi fenomeni è misurabile.Theoretical and experimental implications in the theory of special relativity resulting from the assumption of synchronization criterion (called absolute) other than the standard, are investigated. The choice of the absolute synchronization is justified by considerations of epistemological status of phenomena such as length contraction and time dilation. The absolute synchronization provides a different interpretation of the theory and is an extension of the scope of special relativity as it can be implemented even in accelerated frames of reference. Therefore it is possible to treat in a unified way the phenomena in both inertial and accelerated frame. The introduction of the absolute synchronization implies a modification of the Lorentz transformations. A characteristic of these new transformations (called inertial) is that the transformation of time is independent of the spatial coordinates . The inertial transformations are obtained in the general case between two systems having (absolute) velocity u1 and u2 in any orientation . It is shown that the inertial transformations can have a group structure if unphysical superluminal frames are considered too. The Born rigid motion of an extended body is analyzed by applying the absolute synchronization. Transformations for electromagnetic fields and the equations of these fields (substituting Maxwell's equations) are derived on the basis of inertial transformations. It is shown that these equations contain solutions in the absence of charges that propagate through space as waves generally anisotropic as provided by the inertial transformations in the propagation of light. The application of electromagnetic theory to accelerated systems show the existence of phenomena never observed before. These phenomena, although not in contradiction with standard relativity, force the interpretation of the theory. An experiment in which one of these phenomena is measurable is proposed and described in this thesis.
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Brighi, Massimo <1954>. "Implicazioni teoriche e sperimentali della sincronizzazione assoluta nella teoria della relatività speciale." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amsdottorato.unibo.it/6232/.
Full textAbstract:
Sono indagate le implicazioni teoriche e sperimentali derivanti dall'assunzione, nella teoria della relatività speciale, di un criterio di sincronizzazione (detta assoluta) diverso da quello standard.
La scelta della sincronizzazione assoluta è giustificata da alcune considerazioni di carattere epistemologico sullo status di fenomeni quali la contrazione delle lunghezze e la dilatazione del tempo. Oltre che a fornire una diversa interpretazione, la sincronizzazione assoluta rappresenta una estensione del campo di applicazione della relatività speciale in quanto può essere attuata anche in sistemi di riferimento accelerati. Questa estensione consente di trattare in maniera unitaria i fenomeni sia in sistemi di riferimento inerziali che accelerati.
L'introduzione della sincronizzazione assoluta implica una modifica delle trasformazioni di Lorentz. Una caratteristica di queste nuove trasformazioni (dette inerziali) è che la trasformazione del tempo è indipendente dalle coordinate spaziali.
Le trasformazioni inerziali sono ottenute nel caso generale tra due sistemi di riferimento aventi velocità (assolute) u1 e u2 comunque orientate. Viene mostrato che le trasformazioni inerziali possono formare un gruppo pur di prendere in considerazione anche riferimenti non fisicamente realizzabili perché superluminali.
È analizzato il moto rigido secondo Born di un corpo esteso considerando la sincronizzazione assoluta.
Sulla base delle trasformazioni inerziali si derivano le trasformazioni per i campi elettromagnetici e le equazioni di questi campi (che sostituiscono le equazioni di Maxwell). Si mostra che queste equazioni contengono soluzioni in assenza di cariche che si propagano nello spazio come onde generalmente anisotrope in accordo con quanto previsto dalle trasformazioni inerziali. L'applicazione di questa teoria elettromagnetica a sistemi accelerati mostra l'esistenza di fenomeni mai osservati che, pur non essendo in contraddizione con la relatività standard, ne forzano l'interpretazione. Viene proposto e descritto un esperimento in cui uno di questi fenomeni è misurabile.Theoretical and experimental implications in the theory of special relativity resulting from the assumption of synchronization criterion (called absolute) other than the standard, are investigated. The choice of the absolute synchronization is justified by considerations of epistemological status of phenomena such as length contraction and time dilation. The absolute synchronization provides a different interpretation of the theory and is an extension of the scope of special relativity as it can be implemented even in accelerated frames of reference. Therefore it is possible to treat in a unified way the phenomena in both inertial and accelerated frame. The introduction of the absolute synchronization implies a modification of the Lorentz transformations. A characteristic of these new transformations (called inertial) is that the transformation of time is independent of the spatial coordinates . The inertial transformations are obtained in the general case between two systems having (absolute) velocity u1 and u2 in any orientation . It is shown that the inertial transformations can have a group structure if unphysical superluminal frames are considered too. The Born rigid motion of an extended body is analyzed by applying the absolute synchronization. Transformations for electromagnetic fields and the equations of these fields (substituting Maxwell's equations) are derived on the basis of inertial transformations. It is shown that these equations contain solutions in the absence of charges that propagate through space as waves generally anisotropic as provided by the inertial transformations in the propagation of light. The application of electromagnetic theory to accelerated systems show the existence of phenomena never observed before. These phenomena, although not in contradiction with standard relativity, force the interpretation of the theory. An experiment in which one of these phenomena is measurable is proposed and described in this thesis.
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COCCIA, LORENZO. "On the planar limit of 3d T_rho^sigma[SU(N)] theories." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/364338.
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In questa tesi discutiamo un limite di particolari teorie di gauge 3d, le teorie T^sigma_rho[SU(N)], che ammetono una descrizione in termini di da quiver. Nel limite considerato, il numero di nodi è grande e i ranghi scalano quadraticamente con la lunghezza del quiver. Le energie libere sulla sfera e il topologically twisted index sono ottenuti usando la procedura della localizzazione supersimmetrica. Entrambi scalano quarticamente con la lunghezza del quiver e quadraticamente con N, con funzioni trilogaritmiche dipendenti dai dati del quiver come coefficienti. Le teorie precedentemente discusse con scaling N^2 \ln N sorgono come casi limite. Le SCFTs IR hanno duali di supergravità ben definiti in Tipo IIB: le energie libere corrispondono esattamente ai risultati olografici e gli indici, nel caso di un twist universale, riproducono correttamente l'entropia di un buco nero universale che può essere immerso nelle soluzioni olograficamente duali. Ogni teoria 3d descritta da un quiver bilanciato è legata ad una 5d, il cui modello matriciale è dominato dallo stesso punto di sella. Ciò conduce a strette relazioni tra osservabili BPS. In particolare, calcoliamo il valore di aspettazione dei Wilson loop in rappresentazioni antisimmetriche, trovando un perfetto accordo con il lato di gravità in un particolare esempio.In this thesis we discuss a limit of 3d T^sigma _rho[SU(N)] quiver gauge theories in which the number of nodes is large and the ranks scale quadratically with the length of the quiver. The sphere free energies and topologically twisted indices are obtained using supersymmetric localization. Both scale quartically with the length of the quiver and quadratically with $N$, with trilogarithm functions depending on the quiver data as coefficients. Previously discussed theories with $N^2 \ln N$ scaling arise as limiting cases. The IR SCFTs have well-behaved supergravity duals in Type IIB: the free energies match precisely with holographic results and the indices, in case of a universal twist, correctly reproduce the entropy of an universal black hole which can be embedded in the holographically dual solutions. Each balanced 3d quiver theory is linked to a 5d parent, whose matrix model is related and dominated by the same saddle point, leading to close relations between BPS observables. In particular, we compute the expectation value of Wilson loops in antisymmetric representations, finding perfect agreement with the gravity side in a particular example.
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Jardim, Marcos Benevenuto 1973. "Aspectos matematicos e fisicos da teoria de Chern-Simons." [s.n.], 1996. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307196.
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Orientador: Alcebiades RigasDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica
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Resumo: O objetivo principal deste trabalho é analisar a aplicação de conceitos geométricos e topológicos à teoria quântica de campos dentro do contexto da teoria de Chern-Simons. Podemos dividí-lo em duas partes. Na primeira parte, revisamos brevemente os conceitos de fibrados com conexão e classes características para definirmos a classe característica secundária de Chern & Simons. Demonstramos que esta é um invariante da estrutura conforme de variedades riemannianas e representa uma obstrução topológica à existência de imersões conformes globais em espaços euclideanos. A segunda parte é dedicada à interação entre geometria, topologia e fisica que surgiu com os trabalhos de E. Witten no período 1988-90. Começamos por analisar a abordagem de Witten ao polinômio de Jones através de uma teoria quântica de campos baseada apenas no termo de ChernSimons. Ainda, esta abordagem permite a generalização do polinômio de Jones para 3-variedades compactas orientáveis. Demonstra-se que esta é uma teoria topológica, ou seja, as quantidades fisicamente relevantes são independentes da escolha de uma métrica. Prosseguimos por observar que a ação de Chern-Simons permite a formulação da relatividade geral em dimensão 2+1 como uma teoria de calibre, possibilitando a quantização do campo gravitacional e transição de topologia do espaço. Finalmente, analisamos o trabalho de Deser, Jackiw & Templeton no qual o termo de Chern-Simons foi primeiro introduzido em teoria de campos. A introdução deste termo na lagrangeana de Yang-Mills provoca o aparecimento de bósons vetoriais massivos e estatística fracionária, entre outros efeitos
Abstract: Not informed
Mestrado
Mestre em Matemática
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Pendeza, Cristiane Aparecida [UNESP]. "Álgebras não associativas octoniônicas e relações extensivas do tipo De Moivre." Universidade Estadual Paulista (UNESP), 2006. http://hdl.handle.net/11449/94308.
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pendeza_ca_me_sjrp.pdf: 785980 bytes, checksum: 9924600af5c466ce74dbb2b6ceddee2e (MD5)O presente trabalho tem por objetivo apresentar uma anþalise dos octônios, bem como da álgebra octoniônica 8-dimensional, que, apesar de não associativos, são descritos para um número de estruturas excepcionais como por exemplo os grupos de Lie excepcionais e suas respectivas álgebras, favorecendo assim o entendimento das rotações de espaços euclidianos de dimensão inferior. Por essa razão se tornam fascinantes em aplicações nas diversas áreas da Matemática e Física. Apresenta-se também uma aplicação dos octônios na analogia da relação clássica de Moivre, e presentes conexões entre funções octoniônicas transcendentais e operadores diferencias da teoria de Fueter.
The objective of this work is to present an analysis of the octonions, as well as the octonionic algebras 8-dimensional. Although they aren't associative, they are described by a number of structures, such as the Lie's exceptional groups and its respective algebras, which help the understanding of rotations of Euclidian spaces of lower dimension. Because of that they are fascinating in applications in several areas of Mathematics and Physics. This work also presents application of octonions in the analog of The Classical De Moivre Relation and presents connections between octonionic transcendent functions and di erential operators of Fueter Theory.
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KAWAKATSU, Marcelo Nobuyuki. "Otimização de antenas lineares e planares para aplicações em sistemas de banda larga." Universidade Federal do Pará, 2009. http://repositorio.ufpa.br/jspui/handle/2011/3437.
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FAPESPA - Fundação Amazônia de Amparo a Estudos e Pesquisas
O objetivo deste trabalho é a otimização da largura de banda de antenas linear e planar para aplicações em sistemas de banda larga. Nesse sentido, foi feito um estudo das técnicas de análise, aumento da largura de banda e otimização adequadas para o problema em questão. Como técnica de análise, foi utilizado o método dos momentos, o qual está apresentado no capítulo II. Para aumentar a largura de banda, foram utilizadas as técnicas de colocação de elementos parasitas e construção de fendas no radiador, descritos sucintamente no capítulo III. Como algoritmo de otimização, foi utilizado o algoritmo genético, descrito sucintamente no capítulo II. Neste trabalho, são apresentadas duas propostas de antenas, uma antena dipolo linear combinada com quatros espiras parasitas, capítulo IV, e uma antena planar do tipo espira, capítulo V. No primeiro caso, foram utilizados elementos parasitas e o algoritmo genético para aumentar a largura de banda e, no segundo, foram empregadas fendas no radiador e a otimização paramétrica para este objetivo.
The objective of this work is the bandwidth optimization of linear and planar antennas for broadband system applications. For achieving this goal, it was made a study of the analysis, bandwidth enlargement and optimization techniques appropriated for the problem in question. As analysis technique, the method of moments was utilized, which is presented in chapter II. For bandwidth enlargement, the techniques of collocation of parasitic elements and building slots in the radiator were employed, briefly described in chapter III. As optimization algorithm, the genetic algorithm was utilized, briefly described in chapter II. In this work, two antenna proposals are presented, a linear dipole antenna combined with four parasitic elements, chapter IV, and a planar antenna of loop type, chapter V. In the first case, it was utilized parasitic elements and the genetic algorithm to enlarge the bandwidth, and in the second, it was employed slots in the radiator and the parametric optimization to this objective.
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BERATTO, EMANUELE. "Infrared properties of three dimensional gauge theories via supersymmetric indices." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2023. https://hdl.handle.net/10281/402369.
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The thesis focuses on the study of various supersymmetric three-dimensional gauge theories, mainly with at least N = 3 supersymmetry.
We range between very different theories and discuss several different aspects with the aim of validate our assumptions. Therefore, the leitmotiv of this work resides not so much in the topics we cover, but rather in the method that we use to obtain such results. This, in fact, consists in analysing the gauge invariant operators of the theory forming the so-called chiral ring. By having access to the chiral ring structure of the theory and to the operators forming it, we gain insight to the properties that needed to confirm or debunk our hypothesis.
We will essentially use two different tools for counting and studying such chiral operators: the Hilbert series and the three-dimensional superconformal index.
Thanks to the Hilbert series, we propose a quiver description for the mirror theories of the circle reduction of four-dimensional twisted χ(a2N) theories of class S. These mirrors are, in fact, described by "almost" star-shaped quivers containing both unitary and orthosymplectic gauge groups, along with hypermultiplets in the fundamental representation.
On the other hand, by means of the superconformal index, we investigate the N = 2 preserving exactly marginal operators of the so called S-fold theories. In particular, we focus on two families of such theories, constructed by gauging the diagonal flavour symmetry of the T(U(N)) and T[2,12][2,12 ](SU(4)) theories. In addition, we also examine in detail the zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis theories, with at least N = 6 supersymmetry, and with both orthosymplectic and unitary gauge groups. A number of dualities among all these theories are discovered and studied using the aforementioned tools.The thesis focuses on the study of various supersymmetric three-dimensional gauge theories, mainly with at least N = 3 supersymmetry. We range between very different theories and discuss several different aspects with the aim of validate our assumptions. Therefore, the leitmotiv of this work resides not so much in the topics we cover, but rather in the method that we use to obtain such results. This, in fact, consists in analysing the gauge invariant operators of the theory forming the so-called chiral ring. By having access to the chiral ring structure of the theory and to the operators forming it, we gain insight to the properties that needed to confirm or debunk our hypothesis. We will essentially use two different tools for counting and studying such chiral operators: the Hilbert series and the three-dimensional superconformal index. Thanks to the Hilbert series, we propose a quiver description for the mirror theories of the circle reduction of four-dimensional twisted χ(a2N) theories of class S. These mirrors are, in fact, described by "almost" star-shaped quivers containing both unitary and orthosymplectic gauge groups, along with hypermultiplets in the fundamental representation. On the other hand, by means of the superconformal index, we investigate the N = 2 preserving exactly marginal operators of the so called S-fold theories. In particular, we focus on two families of such theories, constructed by gauging the diagonal flavour symmetry of the T(U(N)) and T[2,12][2,12 ](SU(4)) theories. In addition, we also examine in detail the zero-form and one-form global symmetries of the Aharony-Bergman-Jafferis theories, with at least N = 6 supersymmetry, and with both orthosymplectic and unitary gauge groups. A number of dualities among all these theories are discovered and studied using the aforementioned tools.
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Deleidi, Laura. "Studio degli aspetti teorici e fenomenologici della fisica di particelle." Doctoral thesis, Università degli studi di Bergamo, 2019. http://hdl.handle.net/10446/128587.
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In questa tesi sono state indagate le condizioni cinematiche e dinamiche in cui potrebbero essere rilevati possibili
neutrini superluminali ossia con massa quadrata negativa emessi nel decadimento binario di pioni. Si è ricavato che
sopra un'energia di soglia pionica il comportamento dell'energia dei neutrini tachionici rispetto all'angolo di emissione
cambia drasticamente rispetto al caso bradionico ordinario; in particolare, sopra l'energia di soglia, che dipende dalla massa del neutrino, si potrebbe osservare anche un'emissione trasversale (angoli maggiori di 90o), proibita per
neutrini ordinari. Questo potrebbe costituire una chiara evidenza per i neutrini superluminali.
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De, Maria Giovanna. "Matematica e musica grafi, tonnetz e teorie neo-riemanniane." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12043/.
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Il primo capitolo verte su argomenti di musica e, dopo una breve premessa generale, ed alcuni cenni biografici di J. S. Bach, si passa ad una analisi strutturale di tipo aritmetico e geometrico su alcune sue famose composizioni, sottolineando in particolare la passione del grande compositore per la numerologia, esaminando l’importanza che il fattore numerologico sempre assume nelle sue opere.
Il secondo capitolo verte su argomenti di matematica e tratta alcuni importanti aspetti della teoria dei grafi, del toro e dell’immersione di grafi in superfici.
Il terzo capitolo, nel quale si fa riferimento agli argomenti dei primi due capitoli, è diviso in tre parti: la prima esamina alcuni principali fondamenti matematico-musicali, la seconda propone un excursus storico dalla scala pitagorica al temperamento equabile, la terza approfondisce il ciclo delle quinte, il Tonnetz e le teorie neo-riemanniane.
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Pettinari, Paolo. "Teorie della gravitazione f(R)." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/9118/.
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Tra tutti i fenomeni naturali osservabili, ne era presente uno particolarmente interessante e con il quale si aveva diretto contatto quotidianamente: la gravità.
Dopo le innumerevoli osservazioni astronomiche effettuate da Galileo, fu Newton nel diciassettesimo secolo a capire che il moto dei pianeti era governato dalle medesime leggi che descrivono la caduta dei gravi sulla Terra e fu quindi lui che ci fornì una prima teoria della gravità con la quale si spiegarono le orbite dei pianeti con ottima precisione.
Grazie al contributo di Einstein, la teoria si rinnovò e si arricchì, ma rimase pur sempre lontana dall' essere completa, tant' è che ancora oggi sono presenti molte domande a cui non siamo in grado di rispondere. In questo articolo ci occuperemo di tali quesiti, provando a formulare una teoria che sia in accordo con le attuali evidenze sperimentali.
Nella prima parte, tratteremo le ragioni che hanno spinto i ricercatori ad introdurre le nuove teorie della gravità f(R); in particolare vedremo la peculiarità delle curve di rotazione delle galassie e perché ci sia il bisogno di tirare in ballo la materia oscura. Discuteremo anche alcuni problemi derivanti dall' evoluzione cosmica e altre incongruenze riguardanti la stabilità delle stelle di neutroni.
In seguito mostreremo come ricavare l' equazione di Einstein partendo dai principi variazionali di Hamilton, e estenderemo tale ragionamento con lo scopo di ottenere un' equazione corrispondente ad una gravità modificata.
Infine, verranno introdotte le teorie della gravità f(R), per mezzo delle quali cercheremo di discutere alcune possibili spiegazioni alle problematiche mosse nella parte introduttiva.
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Santos, Nilson Diego de Alcantara [UNESP]. "As origens da teoria dos invariantes na Inglaterra e o Mécanique Analytique de Lagrange (1788)." Universidade Estadual Paulista (UNESP), 2014. http://hdl.handle.net/11449/91052.
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000755405.pdf: 721229 bytes, checksum: a665c9ee190d3a2675b924dd4bb2c525 (MD5)As origens da Teoria dos Invariantes na Inglaterra e o Mécanique Analytique de Lagrange (1788), é um trabalho voltado principalmente a entender uma possível influência que levou George Boole em 1841, a escrever o artigo Exposition of a General Theory of Linear Transformations e verificar se a motivação que o fez produzir este trabalho é igual ou diferente da motivação que ele exerceu sobre Arthur Cayley e consequentemente sobre James Joseph Sylvester. O presente trabalho apresenta um estudo das origens da Teoria dos Invariantes, no século XIX na Inglaterra. De acordo com os historiadores da Matemática o marco do início desta Teoria foi a publicação de George Boole em 1841. Assumimos este artigo como referência principal para realizar nossa pesquisa. Analisamos “antes” e “após” esta publicação de 1841. Concluímos que o Mécanique Analytique de Lagrange, foi a principal motivação para George Boole escrever seu trabalho e, certamente, George Boole foi uma grande influência para Arthur Cayley no que condiz com a escolha do assunto “invariantes” bem como o desenvolvimento desta Teoria por Cayley
The origins of the theory of invariants in England and Mécanique Analytique of Lagrange (1788), is a work geared primarily to understand a possible influence that led George Boole in 1841, writing the article Exposition of the General Theory of Linear Transformations and verify that the motivation that did produce this work is equal or different of the motivation that he exerted on Arthur Cayley and James Joseph Sylvester consequently. This paper presents a study of the Invariant Theory origins, in the nineteenth century in England. According to historians of Mathematics the beginning of this Theory was the publication in 1841 of George Boole. We have taken this article as a reference to our research. We have proposed to analyzed before and after this publication, 1841. We conclude that the Mécanique Analytique Lagrange, was the essential motivation for George Boole write his work, and certainly George Boole was a great influence to Arthur Cayley in which matches the choice of subject invariants as well as the development of this Theory by Cayley
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KAWAKATSU, Marcelo Nobuyuki. "Superfícies eletromagnéticas de microondas com controle do regime de trapped-mode." Universidade Federal do Pará, 2012. http://repositorio.ufpa.br/jspui/handle/2011/3007.
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CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho foram investigadas (FSSs) com ressonância de alto fator de qualidade (fator Q) e independência da polarização para uma onda plana com incidência normal. Estas FSSs são baseadas em um arranjo planar de metalizações sobre um substrato. Um alto fator Q é obtido por meio da excitação do trapped-mode e a independência da polarização, por meio da alta simetria rotacional dos elementos que compõe o arranjo. Para o projeto de FSSs com controle do regime de trapped-mode, foram utilizados substratos feitos de materiais com possibilidade de controle de suas propriedades elétricas ou magnéticas (ferrite magnetizada ou silício ativado oticamente). O arranjo de dois anéis concêntricos em um substrato dielétrico analisado neste trabalho apresenta uma ressonância de trapped-mode com fator Q em torno de 12 e transmitância máxima de 70 %. Com a utilização de um substrato de ferrite magnetizada nesse arranjo, é mostrado que é possível deslocar a frequência de ressonância do trappedmode em torno de 20 %, sem degradação significativa da ressonância de transmisão. Com o emprego de um substrato de silício ativado opticamente, é demonstrado que é possível realizar um chaveamento praticamente completo da banda de transmissão desse arranjo. Para realização das simulações computacionais foram utilizados o método dos momentos no domínio espectral (SDMM) e os programas comerciais Ansoft Designer 5 Planar EM e CST 2009.
In this work frequency selective surfaces (FSSs) with high quality factor (Q-factor) resonance and polarization independence for a normally incident plane wave were investigated. These FSSs are based on a planar array of metallization on a substrate. A high Q-factor is obtained by excitation of trapped-mode and polarization independence by means of high rotational symmetry of the elements that compose the array. For the design of FSSs with trapped-mode regime control, substrates made of materials with the possibility of controlling their electric or magnetic properties (magnetized ferrite or optically activated silicon) were used. The two concentric rings array on a dielectric substrate analyzed in this work presents a trapped-mode resonance with a Q-factor around 12 and maximum transmittance of 70 %. With the utilization of a magnetized ferrite substrate in this array, it is shown that we can shift the resonance frequency of the trappedmode around 20 % without significant degradation of the transmission resonance. With the use of an optically activated silicon substrate, it is demonstrated the possibility of an almost complete switching of the transmission band in that array. To perform the computer simulations the spectral domain moment method (SDMM) and the commercial programs Ansoft Designer 5 PlanarEM and CST 2009 were used.
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GARLASCHI, STEFANO. "Approccio fisico-statistico a tematiche ecologiche e biologiche." Doctoral thesis, Università degli studi di Padova, 2021. http://hdl.handle.net/11577/3447313.
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Gli scienziati sono sempre stati attratti dallo studio del fenomeno della vita, poiché essa mostra una pletora di comportamenti curiosi ed enigmatici. In particolare, negli ultimi decenni si è registrato un crescente interesse da parte della comunità composta dai fisici nei confronti dei sistemi ecologici e biologici. Questo deriva dal fatto che la disciplina della Meccanica Statistica offre molti strumenti, framework e idee che si sono rivelati naturalmente adatti, oltre che molto efficienti, per trattare sistemi affetti da un enorme grado di complessità, come sono i sistemi viventi.
In questa tesi abbracciamo tale prospettiva e quindi affrontiamo tematiche bio-ecologiche utilizzando una mentalità meccanico-statistica.
Innanzitutto proponiamo un modello che descrive comunità ecologiche in cui diverse specie competono per il consumo di un pool condiviso di risorse, con l'obiettivo di capire come possa avere origine l'enorme biodiversità che si incontra empiricamente in molti ecosistemi. Per fare ciò, abbiamo esteso il celebre modello di MacArthur per tendere conto in modo efficace di contributi spaziali, originati da una varietà di meccanismi ecologici. Grazie a ciò, dimostriamo analiticamente che la dinamica prevede la coesistenza di diverse specie in competizione per un numero limitato di risorse, in completo accordo con le evidenze provenienti dalle osservazioni empiriche. Questo è dovuto esclusivamente alla modifica che introduciamo, basata su argomenti sia fisici che ecologici, poiché un tale risultato non può essere ottenuto nella formulazione classica del modello.
In seguito, spostiamo la nostra attenzione sullo studio delle caratteristiche universali delle strutture spaziali regolari auto-organizzate, che possono essere trovate in indagini ecologiche sia empiriche che teoriche. Data la loro ampia diffusione anche in altri campi scientifici, ricerchiamo l’esistenza di un comportamento universale nella loro evoluzione spazio-temporale, indipendentemente dalle peculiarità microscopiche che caratterizzano un certo sistema. Forniamo quindi un framework matematico in grado di stabilire se tali pattern emergano o meno. Inoltre, nella fase di pattern-formation del modello, siamo in grado di mostrare che esiste un regime in cui l'evoluzione dell'involucro di tali strutture spaziali su lunghe scale temporali e grandi scale spaziali è indipendente dal modello, cioè che tale evoluzione è governata da un'equazione, la cui forma non dipende dai dettagli della dinamica.
Infine, motivati da scenari biologici reali, costruiamo un quadro teorico che acquisisce la forma di una dinamica di Langevin generalizzata, tenendo conto dei contributi stocastici demografici e degli effetti dei ritardi temporali. Quindi modelliamo sistemi la cui evoluzione, soggetta a effetti stocastici, è determinata anche dagli stati visitati in passato dal sistema. Dimostriamo come un tale framework predica abbastanza naturalmente l'emergere di comportamenti oscillatori quasi regolari, sotto forma di cicli indotti dal rumore, nell'evoluzione temporale del sistema. Applichiamo poi questi risultati teorici per comprendere le evidenze provenienti da esperimenti che studiano reti di regolazione dell'espressione genica all’interno delle cellule, in cui i contributi del rumore e del ritardo sono effettivamente in gioco.Natural scientists have been always attracted by the study of the phenomenon of Life, since it displays a plethora of curious and yet puzzling behaviors. In the last decades it has been registered an increasing interest in the investigations of ecological and biological systems by the Physics community. This stems from the fact that the physical discipline of Statistical Mechanics offers many tools, frameworks and ideas that have turned out to be naturally adapted, as well as very efficient, to deal with systems affected by an huge degree of complexity, like living systems are. In this Thesis we embrace such a perspective and so we tackle ecological and biological topics employing a Statistical Mechanics mindset.% and we focus on three different remarkable features, which are hallmarks of the complex nature of living systems. We firstly model ecological communities in which several different species compete for the consumption of a shared pool of resources with the aim of understanding how the huge biodiversity empirically encountered can originate. To do so, we extended the celebrated MacArthur's consumer-resource model to account for spatial contributions, originating from a variety of ecological mechanisms, in an effective way. Thanks to this, we show analytically the model predicts several species coexisting while competing for a limited number of resources, in complete agreement with evidences coming from empirical observations. This is solely due to the modification we introduce, based on both physical and ecological arguments, since such a result can not be obtained within the classical formulation of the model. Then, we move our attention to study the universal features of self-organized regular spatial structures, which can be found in both empirical and theoretical ecological investigations. Due to their wide diffusion also in other scientific fields, we search for any universal behavior in their spatio-temporal evolution, regardless the microscopic peculiarities characterizing a certain system. We provide a mathematical framework able to state whether such patterns emerge or not. More interestingly, in the pattern formation phase of the model, we are able to show that it exists a regime in which the evolution of the envelope of such spatial structures on long timescales and large spatial scales is model independent, i.e., it is governed by an equation, whose shape does not dependent on the dynamics details. Finally, motivated by real-world biological scenarios, we build a theoretical framework, which acquires the form of a generalized Langevin dynamics, accounting for demographic stochastic contributions and temporal delays effects. Hence we model systems whose evolution, subjected to noisy effects, is determined also by the past states visited by the system. We demonstrate how such a framework predicts quite naturally the emergence of almost regular oscillating behaviors, in the form of noise-induced cycles, in the temporal evolution of the system. We then apply these theoretical findings to understand the experimental results studying gene expression regulatory networks, in which noise and delay contributions indeed are at stake.
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Kozakevich, Daniel Norberto. "Sistemas não lineares da fisica e da engenharia." reponame:Repositório Institucional da UFSC, 1995. http://repositorio.ufsc.br/xmlui/handle/123456789/76239.
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Tese (doutorado) - Universidade Estadual de Campinas, Departamento de Matematica AplicadaMade available in DSpace on 2012-10-16T08:32:59Z (GMT). No. of bitstreams: 0Bitstream added on 2013-07-16T17:24:42Z : No. of bitstreams: 1 100944.pdf: 2681436 bytes, checksum: ec6222871d8589d1aa458a2da32245b7 (MD5)
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Gallo, Rita. "La matematica in fisica tra i banchi di scuola." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020.
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Nonostante gli studenti siano naturalmente predisposti verso le discipline scientifiche, perché le Scienze incuriosiscono ed hanno il fascino della scoperta, il loro insegnamento/apprendimento è in crisi a livello nazionale ed internazionale.
Attraverso l’analisi dell'indagine Pisa si analizzeranno gli apprendimenti degli studenti italiani in Matematica e Scienze.
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SERRA, IRENE. "L'infinito in Aristotele fra fisica, matematica e metafisica." Doctoral thesis, Università degli Studi di Cagliari, 2020. http://hdl.handle.net/11584/295011.
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Only recently scholars focus their attention on "Physics"’ Gamma - which deals with the treatment of movement and infinity. In the second half of the twentieth century, there has been a growing interest in the Aristotelian infinity, and therefore in "Physics": is Aristotle's infinity a reality of the noetic sphere, or is it a reality external to thought, belonging to the sphere of experience? Is Aristotelian infinity mere potentiality and negativity, or can we see a certain "actuality" in its existence?
In my investigation, I focus not only on an ontological perspective: rather, I will try to highlight how to achieve an adequate understanding of infinity by taking into account physical-cosmological, mathematical-geometric and also metaphysical problems.
However, this perspective on the problem of infinity does not suggest that for Aristotle there are three different infinities, but one and the same infinite: the infinite presented in "Phys." Γ and the one presented in "Phys." Θ are not in a contradictory relationship with each other, but they complete and explain each other.
Finally, Aristotle's ἄπειρον must be conceived as the result of the intertwining of the three different theoretical dimensions of physics, mathematics and metaphysics, all of which are not in a relationship of strong separation, but in a fluid and interconnected relationship.
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Bressan, Lisa. "Il bello in Aristotele. Fisica, matematica, filosofia prima." Doctoral thesis, Università degli studi di Padova, 2007. http://hdl.handle.net/11577/3425186.
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Capriolo, Maurizio. "Lo pseudotensore energia-impulso in teorie estese della gravitazione." Doctoral thesis, Universita degli studi di Salerno, 2018. http://elea.unisa.it:8080/xmlui/handle/10556/4238.
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2016 - 2017The gravitational field’s energy and momentum definitions are treated in extensive gravitation theories, through the generalization of the energymomentum pseudotensor, defined by Einstein in general relativity. This extension was obtained by modifying the Lagrangian of Hilbert-Einstein or by using a different connection from the one of Levi- Civita as that of Weitzenböck for teleparallel theories. We have firstly obtained the gravitational energy-momentum pseudotensor for extended Lagrangians that depend on the metric gμ⌫ and on its derivatives up to nth order and then demonstrated, in general, its affine and non-covariant behavior. Then we applied the weak field limit to Euler-Lagrange equations associated to the Lagrangian which depends linearly on the ⇤R terms and derived the modified gravitational waves with six polarization states, three transverse and three not, with helicity 0 and 2. Subsequently we have obtained, through the Noether theorem for infinitesimal rigid translations, the relative energy-momentum pseudotensor and after having developed it to the order h2 and mediated on an suitable domain, we have calculated the power emitted from a possible gravitational radiant source. For gravity f (R) and f (T) we have obtained the respective energy-momentum pseudotensors and, via the border therm B which connects the curvature R to the torsion T, we have studied the relative pseudotensor ⌧↵ #|!(T,B) allowing us to link ⌧↵ #|f(R) and ⌧↵ #|f(T). Finallywehave obtained the equations for two theories of higher order telepallel gravity: in particular for the Lagrangian L⇤kT = h ! T + Pp k=0 akT⇤kT # and for the sixth order telepallel gravity equivalent to LR⇤R = p−g (−R + a0R2 + a1R⇤R). [edited by author]
XXX n.s.
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Dandrea, Lucia. "Quantum Monte Carlo Methods applied to strongly correlated and highly inhomogeneous many-Fermion systems." Doctoral thesis, Università degli studi di Trento, 2009. https://hdl.handle.net/11572/369209.
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Bausmerth, Ingrid. "Fermi Mixtures: Effects of Engineered Confinements." Doctoral thesis, Università degli studi di Trento, 2009. https://hdl.handle.net/11572/368660.
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In this thesis we first review the theory of the normal state of the unitary Fermi gas at T = 0 and the main properties of the normal-to-superfluid transition. Then we study the trapped gas under adiabatic rotation, i.e., avoiding the formation of vortices. We show that for polarized systems the rotation enhances the Chandrasekhar-Clogston limit due to pair breaking at the border between the superfluid and the normal phase, while it leaves the global critical polarization Pc of the trapped system unaffected. In the case of an unpolarized unitary superfluid the rotation causes a phase separation between a superfluid core and an unpolarized normal shell, in which the densities of the spin-up and spin-down atom numbers is equal. For both the polarized and the unpolarized systems we calculate experimental observables such as the density profiles and the angular momenta. From the study of Bose-Einstein condensates it is well known that an adiabatic
rotation induces a quadrupole deformation of the trapped atomic cloud when the rotation exceeds a certain angular velocity. In Fermi gases the situation is different due to the phase separation discussed above, and the quadrupole
instabilities are found to set on at smaller angular velocity than in the BEC case. This phenomenon together with a more general discussion concerning not only the energetic but also the dynamic instabilities of the phase separated system is presented. We use the present knowledge of the equation of state of Fermi mixtures with unequal masses to give quantitative predictions for the phase separation between the normal and superfluid components. The analysis is based on the study of the zero temperature μ-h phase diagram of the uniform two component gas. The phase diagram at unitarity is determined thanks to the knowledge of the equation of state available from diagrammatic techniques applied to highly polarized configurations and from Monte Carlo simulations. The phase diagram is then used, in the local density approximation,
to calculate the density profiles of the two Fermi components in the presence of harmonic trapping. Eventually we investigate the polarization produced by the relative displacement of the potentials trapping two spin species of a unitary Fermi gas with population imbalance. We investigate the dipole polarizability of a polarized system both in the two-fluid and the three-fluid model at zero temperature and point out the major differences between the two treatments.
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Marin, Diego. "From the Hamiltonian formalism to the Spin-Foams: The final step in LQG?" Doctoral thesis, Università degli studi di Trento, 2010. https://hdl.handle.net/11572/368076.
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Already in ancient Greece, the pre-Socratic philosophers thought that natural phenomena, although different, were homogeneous, of the same fundamental nature. In their theories can be found the search for a common reference point (arché) that puts order in the chaotic multiplicity of phenomena. After Albert Einstein’s theory of gravitation (General Relativity -GR-) was published in 1915, the search for a unified field theory that combines gravity with electromagnetism began to become serious. It seemed plausible that there were no other fundamental forces. The main contributors were Gunnar Nordstrom, Hermann Weyl, Arthur Eddington, Theodor Kaluza, Oskar Klein (See Theory of Kaluza-Klein, 1921) and most notably the many attempts by Einstein
and his collaborators. No attempt went through. In the first half of the twentieth century quantum mechanics was consolidated, an instrument capable of overcoming the inadequacy of classical mechanics to explain phenomena and properties such as blackbody radiation, the photoelectric effect, the specific heat of solids, the atomic spectra, the stability of atoms, the Compton effect, .... When in the thirties Fermi and Yukawa ’s studies led to the discovery of nuclear forces, the quantum formalism proved to be appropriate for the description of the new phenomena and, in 1967-68, Sheldon Glashow, Steven Weinberg and Abdus Salam showed how the weak nuclear
force and the electromagnetism were simply different manifestations of the same force (electroweak). Since then, proposals have been done to include in a single grand unification theory also the strong nuclear force, and some of them (GTU SU(5) and SO(10)) have provided testable predictions as the quantization of electric charge. At classical level there is an extension of the Kaluza-Klein theory on a 11-dimensional space M4 × S1 × S2 × CP2. It corresponds to Einstein’s General Relativity with 7 extra dimensions, and considers all four forces as different expressions of a “mega†gravitational field. The forces are unified at the classical level but, once quantized,
the theory turns out to be inconsistent and therefore unusable. This is because the nuclear forces have range of 10−15 m for strong force and of 10−18 m for weak force, distances at which classical physics loses its meaning. Ultimately, it seems that quantum mechanics is compatible with electroweak and strong interactions only if we limit ourselves to spaces of dimensionality less than or equal to 4. In addition, it is inconsistent with General Relativity for spaces with more of 3 dimensions. For these reasons, the theory of Kaluza-Klein fails doubly. Really, the incompatibility is not between general relativity and quantum mechanics in its entirety, but rather between General
Relativity and the method of calculation used in quantum mechanics: perturbative expansion whose terms, in the cases indicted above, become . To get around this problem two different approaches have been taken: String Theory and Loop Quantum Gravity. The first has completely changed the wording of quantum theory, from considering local interactions, where the phenomena occur at specific points (of Feynman graphs), to interactions “extended†, where the phenomena are distributed along one limited dimension (string), open or closed. This system has eliminated the divergences in the terms of perturbative expansion, but has developed other anomalies, eliminated only by building up the theory on a space of 11 dimensions. Unfortunately, the extra dimensions introduce a huge number of arbitrariness, such as the theory can predict
everything and nothing. The scientific community hopes to identify some potential whose minimum make a selection between these arbitrariness, but we are still far from such a result. The alternative discussed in this thesis is the Loop Quantum Gravity.
This is simply the union of GR and quantum mechanics, without modifying the basic axioms of both. It can be made only in spaces of dimensionality equal to 4 and it surrenders completely the perturbative expansion. This produces fascinating predictions, such as the inflation of early universe, and the lack of singularities in the black holes and in the big bang. It also provides the picture of a “combinatorial†universe, described by nodes connected by paths, whose only necessary variables are integer numbers associated with nodes and paths. This last point in particular escapes the string theory which, whilst losing the locality, is however concentrated within the “very small†. The Loop Quantum Gravity, by contrast, is able to describe the universe as a whole, and to deal with transitions between universes of different topology. The downside is that the calculations are so complex that they are impracticable. Strategies have been developed
to introduce a different perturbative expansion that makes the calculations feasible, but this introduces important changes to the initial structure of the theory, in a way that eliminate the beautiful cosmological predictions. Nevertheless, we tried to calculate the graviton propagator in this new “modified framework†, and the result is compatible with linearized quantum GR . For this reason, this framework has not been abandoned. It also seems that this formalism can easily be extended to include extra-dimensions and adapted to the unified theory of Kaluza Klein.
This thesis has been developed in an attempt to contribute to the desire for simplification and connection to the essence that has always been in the natural sciences. In particular, it was given a demonstration of how the †modified framework†of Loop Quantum Gravity is derivable from a classical formulation of the GR of Palatini type.
Finally, we give suggestions for extending the model to 11 dimensions, because 11 is the number suggested by String theory, by the classical theory of Kaluza Klein, and by the GTU SO(10). Probably the truth lies somewhere in between, maybe an action of a 4-dimensional brane immersed in a 11-dimensional universe would be the right compromise between String Theory and Loop Quantum Gravity. A 4-dimensional brane represents our universe, and any contact with other branes of a much smaller scale put small pieces of it in vibration. Depending on the number of dimensions in which contact is, the part could be a vibrating string or a two- or three-brane (with probability decreasing rapidly moving from string to the three-brane). So, we even lose the distinction between the notions of particles and universes, making the first totally unnecessary. The action of a 4-brane is equivalent to the action of Loop Quantum Gravity, with the coordinate-fields which assume the role of gauge fields, and the indexes in the 11-dimensional space that would become similar to the indexes of internal gauge. This thesis focuses on two specific problems: the calculation of the graviton propagator in Loop Quantum Gravity and the derivation of the “modified framework†from the Palatini formulation of GR (Chapter 8). While the first it was
simply supported with a minimum contribution, the second is a problem undertaken by the student in a completely independent way that, while waiting for more in-depth audits, has not yet shown any inconsistency and for now can be hailed a success. A small space is reserved for some inedited consideration undertaken by the student on the “physical†projector. This operator is intended to project the Hilbert space of kinematic states in the subspace of physical states. The conclusion of the argument is simple and somewhat disturbing: the Loop Quantum Gravity is not an unitary theory!
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Di, Criscienzo Roberto. "Semi-classical aspect of black hole physics." Doctoral thesis, Università degli studi di Trento, 2011. https://hdl.handle.net/11572/367865.
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Autieri, Emmanuel. "Development of Free Energy Calculation Methods for the Study of Monosaccharides Conformation in Computer Simulations." Doctoral thesis, Università degli studi di Trento, 2011. https://hdl.handle.net/11572/368084.
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This thesis is devoted to the study of the conformation of monosacchrides in six-membered ring form. The main goal is to develop and apply new computational tools to investigate conformational properties and to improve the description of carbohydrates in the framework of molecular dynamics simulations.
In the field of monosaccharides, modeling the system within the molecular dynamics framework presents troublesome aspects. The most important issue is that some force fields (e.g., the chosen gromos 45a4 parameter set) fail in reproducing the conformational preferences of the sugar constituents, with the appearance of unphysical conformations. This lack stems from the fact that the conformational behavior, dominated by few structures, generates a severe bottleneck: the non-ergodicity of the system by any practical means. This aspect explains the interest in free energy calculations, and methods exist, such as umbrella sampling or metadynamics, that allow to accelerate the sampling of different conformations by adding bias forces. In general, accelerated sampling methods are based on the choice of collective variables (CVs), which is of particular importance for the proper reconstruction of free energy landscapes. In the field of conformational analysis, suitable CVs have to be considered to describe non-planar, puckered conformations of cyclic structures.
One of the main goals of this work is the enhancement of the gromos 45a4 force field for carbohydrates, with respect to the ability to describe ring conformation (that is, puckering) of six-membered rings. To this end, the development of efficient computational tools for the investigation of the general puckering problem are presented. In particular, we indicate how to exploit the capabilities of the metadynamics algorithm applied to the investigation of puckered ring conformers, exploring also different parametrizations of puckered structures to assess their respective advantages as collective variables for metadynamics.
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Sebastiani, Lorenzo. "General Aspects of Modified Theories of Gravity." Doctoral thesis, Università degli studi di Trento, 2011. https://hdl.handle.net/11572/367870.
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The aim of this work is to investigate the both, some mathematical and physical general aspect of modified gravity, and, more specifically, the proprieties of viable, realistic models of modified gravity which can be used to reproduce the inflation and the dark energy epoch of universe today.
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Acquaviva, Giovanni. "Tunnelling and Unruh-DeWitt methods in curved spacetimes." Doctoral thesis, Università degli studi di Trento, 2013. https://hdl.handle.net/11572/368925.
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The analysis and the results contained in this work are rooted in a first contact between the quantum theory and the general theory of relativity. By first contact it is meant that we are not considering candidates for “unified theories", but rather we focus on aspects of the full quantum theory in changing geometric backgrounds: the analysis of such an interaction already had important applications in cosmology, e.g. in the description of the evolution of fields in inflationary scenarios. Another compelling – and still growing – area of application is the study of thermodynamical properties of gravitional systems, which covers the main bulk of this thesis.
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Forini, Valentina. "Non trivial string backgrounds: Tachyons in String Field Theory and Plane-waves in DLCQ Strings." Doctoral thesis, Università degli studi di Trento, 2006. https://hdl.handle.net/11572/368486.
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One of the most interesting problems in string theory is to understand how the background space-time on which the string propagates arises in a self-consistent way. For open strings, there are two main approaches to this problem, boundary string field theory (BSFT) and cubic string field theory (CSFT). In the first part of this Thesis we deal with the construction of the spacetime tachyon effective action in BSFT. Renormalization fixed points are solutions of classical equations of motion and should be viewed as solutions of classical string field theory. We have constructed the Witten-Shatashvili (WS) space-time action S and shown that some solitonic solutions are lower dimensional D-branes for which the finite value of S provides a quite accurate prediction of the D-brane tension. We have derived the explicit relation between the CSFT and WS action as a field redefinition which is nonsingular on-shell only when the normalization factor in the WS action coincides with the tension of the D25-brane, in agreement with the conjectures involving tachyon condensation. We have also found a time-dependent solution of CSFT whose evolution is driven by a diffusion equation that makes the equations of motion local with respect to the time variable. The analysis here proposed has attracted a good deal of attention for its potential cosmological applications. The profile can be expressed in terms of a series in powers of exponentials of the time coordinate, and gives evidence of a well-defined but wildly oscillatory behavior. The tachyon rolls well past the minimum of the potential, then turns around and begins to oscillate with ever increasing amplitude. Furthermore, we have derived an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude. From such a solution we computed the exact coefficient of the quartic effective action relevant for time-dependent solutions and we derived the exact coefficient of the quartic tachyon coupling. We studied the rolling tachyon solution expressed as a series of exponentials of the time coordinate both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level-truncated coefficients converge to those derived using the exact string amplitude and confirm the wild oscillatory behavior.
In the second part of the Thesis we consider the extension of the gauge/gravity correspondence to systems with reduced and hence more realistic supersymmetry, which is one of the main steps towards a non-perturbative description of confining, QCD-like, gauge theories in terms of gravitational backgrounds. If string theory on AdS5xS5 is integrable, the theory on simple orbifolds of that space would also be expected to be integrable. We have computed the planar finite size corrections to the spectrum of the dilatation operator acting on states of a certain limit of conformal N = 2 quiver gauge field theory which is a ZM-orbifold of N = 4 SYM theory. We matched the result to the string dual, IIB superstrings on a pp-wave background with a periodically identified null coordinate. Up to two loops, we have shown that the computations done by using an effective Hamiltonian technique and a twisted Bethe Ansatz agree with each other and also agree with a computation of the analogous quantity in string theory. Our results are consistent with integrability of the N = 2 theory.
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Zou, Peng. "Mean-field theory for the dynamics of superfluid fermions in the BCS-BEC crossover." Doctoral thesis, Università degli studi di Trento, 2014. https://hdl.handle.net/11572/368592.
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We use mean-field theory to investigate the dynamics of superfluid fermions. This thesis includes our two works.
The first one is to study Josephson oscillations and self-trapping of superfluid fermions in a double-well potential with time-dependent Bogoliubov-de Gennes equations. We investigate the behaviour of a two-component Fermi superfluid. We numerically solve the time-dependent Bogoliubov-de Gennes equations and characterize the regimes of Josephson oscillations and self-trapping for different potential barriers and initial conditions. In the weak link limit the results agree with a two-mode model where the relative population and the phase difference between the two wells obey coupled nonlinear Josephson equations. A more complex dynamics is predicted for large amplitude oscillations and large tunneling. The second one is to calculate the dynamic structure factor of unitary fermions. We have studied the dynamic structure factor of unitary fermions both at zero and finite temperature using the Bogoliubov-de Gennes theory and also Superfluid Local Density Approximation. We have derived the expression of the linear response function and the dynamic structure factor in the random phase approximation. At zero temperature, the SLDA+RPA formalism indeed provides a better accuracy at low momentum transfer and also its static structure factor is closer to quantum Monte Carlo value than that in BdG+RPA; however SLDA seems to give worse results for the molecular excitations at large momentum transfer. We have discussed the role of temperature and the comparison between SLDA and BdG, as well as with experimental data. The analysis is still at a preliminary level, but it suggests that mean-field theories can indeed be used to extract quantitative
information about the order parameter and the excitations of the system by two-photon Bragg scattering experiments.
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Sartori, Alberto. "Dynamical properties of Bose-Bose Mixtures." Doctoral thesis, Università degli studi di Trento, 2016. https://hdl.handle.net/11572/369114.
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In this Thesis is presented a study on dynamical properties of mixtures of ultraold Bose gases. The behaviour of this system in different regimes is analysed: with and without coherent coupling between the two components, in homogeneous and harmonic shaped trapping potentials and in different dimensions and geometries. Most of the results presented here have been obtained by means of numerical solutions of coupled Gross-Pitaevskii equations and have been compared with theoretical predictions (and sometimes experiments), describing the same phenomena. In particualr the stability of persistent currents in a two-component Bose-Einstein condensate in a toroidal trap is studied in both the miscible and the immiscible regime. In the miscible regime we show that superflow decay is related to linear instabilities of the spin-density Bogoliubov mode. We find a region of partial stability, where the flow is stable in the majority component while it decays in the minority component. We also characterize the dynamical instability appearing for a large relative velocity between the two components. In the immiscible regime the stability criterion is modified and depends on the specific density distribution of the two components. The effect of a coherent coupling between the two components is also discussed. A study on the collective modes of the minority component of a highly unbalanced Bose-Bose mixture is also presented. In the immiscible case we find that the ground state can be a two-domain walls soliton. Although the mode frequencies are continuous at the transition, their behaviour is very different with respect to the miscible case. The dynamical behaviour of the solitonic structure and the frequency dependence on the inter- and intra-species interaction is numerically studied using coupled Gross-Pitaevskii equations. The results of the study on the static and the dynamic response of coherently coupled two component Bose-Einstein condensates due to a spin-dipole perturbation is also sown. The static dipole susceptibility is determined and is shown to be a key quantity to identify the second order ferromagnetic transition occurring at large inter-species interactions. The dynamics, which is obtained by quenching the spin-dipole perturbation, is very much affected by the system being paramagnetic or ferromagnetic and by the correlation between the motional and the internal degrees of freedom. In the paramagnetic phase the gas exhibits well defined out-of-phase dipole oscillations, whose frequency can be related to the susceptibility of the system using a sum rule approach. In particular in the interaction SU (2) symmetric case, when all the two-body interactions are the same, the external dipole oscillation coincides with the internal Rabi flipping frequency. In the ferromagnetic case, where linear response theory is not applicable, the system shows highly non-linear dynamics. In particular we observe phenomena related to ground state selection: the gas, initially trapped in a domain wall configuration, reaches a final state corresponding to the magnetic ground state plus small density ripples. Interestingly, the time during which the gas is unable to escape from its initial configuration is found to be proportional to the square root of the wall surface
tension.
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De, Rosi Giulia. "Collective oscillations of a trapped atomic gas in low dimensions and thermodynamics of one-dimensional Bose gas." Doctoral thesis, Università degli studi di Trento, 2017. https://hdl.handle.net/11572/368019.
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Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity.
In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in
the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids.
Finally, we investigate a gas with a finite number N
of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring
from the one in the large N limit.