Dissertationen zum Thema „Relativistic quantum theory“
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1
Ruschhaupt, Andreas. „A relativistic extension of event enhanced quantum theory“. [S.l.] : [s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=96395864X.
2
Wallace, David. „Issues in the foundations of relativistic quantum theory“. Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270178.
3
Somaroo, Shyamal Sewlal. „Applications of the geometric algebra to relativistic quantum theory“. Thesis, University of Cambridge, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627593.
4
Tagliazucchi, Matteo. „Renormalization in non-relativistic quantum mechanics“. Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21030/.
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A problem of non-relativistic quantum mechanics solved using regularization and renormalization techniques is presented in this thesis. After a general introduction of these techniques, they are applied to a problem in classical electromagnetism and to the bound state of a single quantum particle subjected to a two-dimensional delta-function potential, that is divergent if computed naively solving directly the Schroedinger equation or using the theory of propagators. The regularization techniques used are the cutoff regularization and the dimensional one and they both leads to the same outcome. An effective field theory approach, in which the potential is regularized through the real space scheme, is also presented. After regularization has been performed, the potential is renormalized re-defining the coupling constant. The running of the renormalized coupling constant is also found, i.e. the renormalization group equation.
5
Skaane, Haakon. „Relativistic quantum theory and its applications to atoms and molecules“. Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267921.
6
Al-Naseri, Haidar. „Quantum kinetic relativistic theory of linearized waves in magnetized plasmas“. Thesis, Umeå universitet, Institutionen för fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-150292.
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In this work we have studied linear wave propagation in magnetized plasmas using a fully relativistic kinetic equation of spin-1/2 particles in the long scale approximation. The linearized kinetic equation is very long and complicated, hence we worked with restricted geometries in order to simplify the calculations. The dispersion relation of the relativistic model was calculated and compared with a dispersion relation from a previous work at the semi-relativistic limit. Moreover, a new mode was discovered that survives in the zero temperature limit. The origin of the mode in the kinetic equation was discussed and derived from a non-relativistic kinetic equation from a previous work.
7
Almoukhalalati, Adel. „Applications of variational perturbation theory in relativistic molecular quantum mechanics“. Toulouse 3, 2016. http://www.theses.fr/2016TOU30172.
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Le père même de la mécanique quantique relativiste P. A. M. Dirac a prédit que la version plus réaliste de la mécanique quant ique qu'il a misen place n'offrirait pas beaucoup plus par rapport à la formulation non relativiste de la mécanique quantique lorsqu'il est appliqué à des systèmes atomiques et moléculaires ordinaires. Lorsque la théorie quantique relativiste avait environ 40 années, les gens avaient commencé à recogenize à quel point les effets relativistes peuvent être même pour l'étude des systèmes atomiques et moléculaires. Les effets relativistes se manifestent par la contraction dess atomiques et orbitales p, l'expansion des orbitales d et 1 atomiques, et le couplage spin-orbite. Un exemple classique de l'importance des effets relativistes est la structure de bande d'or métallique pour lequel les calculs non-relativistes vont conduire à une surestimation de l'écart 5d - 6p et prédire une bande d'absorption UV qui est compatible avec un métal qui ressemble à l'argent. La thèse porte sur les calculs atomiques et moléculaires dans le cadre relativiste à 4-composantes. En particulier, l'utilisation de la théorie des perturbations variationnelle dans un cadre relativiste. La théorie des perturbations dans la mécanique quantique, est basée sur le partitionnement du Hamiltonien il en l'Hamiltonien Ho a l'ordre zéro et \Î qui forme la perturbation par le biais d'un paramètre lambda. Dans la théorie des perturbations à N-corps {Rayleigh-Schrodinger), nous disposons d 'une solution exacte de l'Hamiltonien Ho. Alors que dans la théorie des perturbations variationnelle, nous supposons d'avoir une énergie optimisée pour toute valeur du paramètre À. La thèse contient deux projets principaux. Le premier projet concerne la discription de la corrélation électronique dans le cadre relativiste. Dans ce projet, nous nous sommes concentrés sur l'approche perturbative pour dériver des formules necessiry relativiste de l'énergie dans les atomes à deux électrons. L'énergie de corrélation est la différence entre la valeur propre exacte de l'hamiltonien et sa valeur d'attente dans l'approximationHartree-Fock. La valeur propre exacte ne sont pas disponibles, mais dans le domaine non-relativiste la meilleure solution est un Cl complet pour une base donnée. Notre objectif principal, dans ce projet, est de montrer que la meilleure solution de l'équation d'onde pour l' Hamiltonien DiracCoulomb, n'est pas un Cl complète, comme dans le cas non-relativis te, mais un MCSCF q ui utilise un développement Cl en orbitales énergiepositive seulement, mais qui permet la rotation entre les o rbitales d 'énerg ie positive et négative afin d 'optimiser l'opérateur de project ion. Le second projet concerne une étude sur les effets du volume nucléaire dans les spectres de vibration des molécules d iatomiques. Au début desannées 80, le groupe du professeur Eberhardt T iemann à Hanovre a util isé la spectroscopie de rotation avec une haute résolution pour étudier unesérie de molécules diatomiques contenant des atomes lo urds comme le plomb, afin d'établir des constantes spectroscopiques (Re longueur de laliaison, la fréquence vibratoire w. Etc. ) avec une grande précision. Une molécule AB a plusieurs isotopomères selon les isotopes des atomes A etB, et il était bien connu à cette époque que le spectre de chaque isotopomère est légèrement différente en raison des d ifférences de masse entrechaque isotope de l'atomes A et B. Prof. Tiemann et ses collaborateurs découvert que nous devons également ten ir compte de la différence devolume nucléa ire de chaque isotope. Nous fournissons un contrôle indépendant sur les études expérimentales et t héoriques précédentes d'effetsde volume nucléaires en spectroscopie de rotation, notamment re-calcul de la t héorie et des calculs antérieurs de référence par l'état relativiste4-composantes de l'art corrélée calculsThe father of relativistic quantum mechan ics P. A. M. Dirac predicted that, the more realistic version of quantum mechanics that he established wouId not offer much more when compared to the non-relativistic formulation of quantum mechanics when applied to ordinary atomic and molecular systems. When the relativistic quantum theory was around forty years old, people had started to recognize how important relativistic effects can beeven for the study of atomic and molecular systems. Relativistic effects are manifested via the contraction of atomics and p orbitais, the expansion of atomic d and 1 orbitais, and spin-orbit coupling. A classical example on t he importance of relativistic effects is the band struct ure of metallic gold for which non-relativistic caleulations will lead to an overestimation of the 5d-6p gap predicting a UV absorption band which is compatible with a metal that looks like silver. The thesis focuses on the atomic and molecular calculations within the 4-component relativistic framework. Ln particular, the use of the variational perturbation theory in relativistic framework. The perturbation theory in quantum mechanics is based on partitioning the Hamiltonian H into zeroth-order Hamiltonian Ho and V that forms the perturbation through a para meter lambda. Ln many-body (Rayleigh-Sch rodinger) perturbation theory, we have an exact solution of t he Hamiltonian l/0 , whereas in the variational perturbation theory, we assume to have anoptimized energy for any value of the parameter À. The thesis contains two principal projects, the first project concerns the description of the electron correlation in the relativistic framework. Ln this project , we focused on the perturbative approach to derive t he relativistic formulas nece~sary for the energy in two-electron atoms. T hecorrelation energy is the difference between the exact eigenvalue of the Ha mi ltonian and its expectation value in the Hartree-Fock approximation. The exact eigenvalue is not avail able, but in the non- relativistic domain t he best solution is a full Cl for a given basis. Our main goal, in this project , will be to show that the best solution of the wave equation for the embedded Dirac-Coulomb Hamil tonian, is not a Full Cl, as in thenon- relativistic case, but a MCSCF which uses a Cl development in positive-energy orbitais only, but which keeps rotations between the positive and negative energy orbitais to optimize the projection operator. The second project concerns a study of the effects of t he nuclear volume in the vibrational spectra of diatomic molecules. Ln the early 80s, Theg roup of Professor Eberhardt Tiemann in Hanover used the rotational spectroscopy with high resolution to study a series of diatomic molecules containing heavy a toms like lead in order to establish spectroscopie constants (R. Bond length, vibrational frequency W c etc. ) with a great precision. A molecule AB has several isotopomers according to isotopes atoms A and B and it was weil known at that t ime only the spectrum of eachisotopomer is slightly d iffe rent because of the mass differences between each isotope of the atoms A and B. Prof. Tiemann and his collaborators discovered that we must also take into account the difference in nuclear volume of each isotope. We provide an independent check on previous experimental and t heoretical studies of nuclear volume effects in rotational spectroscopy, notably re-derivation of theory and benchmark previous calculations by 4-component relativistic state of the art correlated calculations
8
Bird, Christopher Shane. „Infrared regularization in relativistic chiral perturbation theory“. Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://hdl.handle.net/1828/1062.
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Chiral perturbation theory is a useful tool in the study of low energy reactions involving light particles. However the inclusion of heavy particles in chiral perturbation theory results in large contributions from loop diagrams which violate the standard power counting scheme. We review two methods, referred to as heavy baryon chiral perturbation theory and infrared regularization, which remove the high energy effects of the heavy particles and which therefore do not violate the power counting scheme. We then use these two methods to calculate the amplitude for pion photoproduction to fourth order and prove that the two amplitudes are equivalent.
9
Aiello, Gordon J. „An application of the theory of moments to Euclidean relativistic quantum mechanical scattering“. Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5902.
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One recipe for mathematically formulating a relativistic quantum mechanical scattering theory utilizes a two-Hilbert space approach, denoted by $\mathcal{H}$ and $\mathcal{H}_{0}$, upon each of which a unitary representation of the Poincaré Lie group is given. Physically speaking, $\mathcal{H}$ models a complicated interacting system of particles one wishes to understand, and $\mathcal{H}_{0}$ an associated simpler (i.e., free/noninteracting) structure one uses to construct 'asymptotic boundary conditions" on so-called scattering states in $\mathcal{H}$. Simply put, $\mathcal{H}_{0}$ is an attempted idealization of $\mathcal{H}$ one hopes to realize in the large time limits $t\rightarrow\pm\infty$.
The above considerations lead to the study of the existence of strong limits of operators of the form $e^{iHt}Je^{-iH_{0}t}$, where $H$ and $H_{0}$ are self-adjoint generators of the time translation subgroup of the unitary representations of the Poincaré group on $\mathcal{H}$ and $\mathcal{H}_{0}$, and $J$ is a contrived mapping from $\mathcal{H}_{0}$ into $\mathcal{H}$ that provides the internal structure of the scattering asymptotes.
The existence of said limits in the context of Euclidean quantum theories (satisfying precepts known as the Osterwalder-Schrader axioms) depends on the choice of $J$ and leads to a marvelous connection between this formalism and a beautiful area of classical mathematical analysis known as the Stieltjes moment problem, which concerns the relationship between numerical sequences $\{\mu_{n}\}_{n=0}^{\infty}$ and the existence/uniqueness of measures $\alpha(x)$ on the half-line satisfying
\begin{equation*}
\mu_{n}=\int_{0}^{\infty}x^{n}d\alpha(x).
\end{equation*}
10
Davis, John E. „Application of the Schwinger closed time-path method to relativistic quantum field theory /“. The Ohio State University, 1991. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487694389393565.
11
Mondal, Ritwik. „Relativistic theory of laser-induced magnetization dynamics“. Doctoral thesis, Uppsala universitet, Materialteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-315247.
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Ultrafast dynamical processes in magnetic systems have become the subject of intense research during the last two decades, initiated by the pioneering discovery of femtosecond laser-induced demagnetization in nickel. In this thesis, we develop theory for fast and ultrafast magnetization dynamics. In particular, we build relativistic theory to explain the magnetization dynamics observed at short timescales in pump-probe magneto-optical experiments and compute from first-principles the coherent laser-induced magnetization. In the developed relativistic theory, we start from the fundamental Dirac-Kohn-Sham equation that includes all relativistic effects related to spin and orbital magnetism as well as the magnetic exchange interaction and any external electromagnetic field. As it describes both particle and antiparticle, a separation between them is sought because we focus on low-energy excitations within the particle system. Doing so, we derive the extended Pauli Hamiltonian that captures all relativistic contributions in first order; the most significant one is the full spin-orbit interaction (gauge invariant and Hermitian). Noteworthy, we find that this relativistic framework explains a wide range of dynamical magnetic phenomena. To mention, (i) we show that the phenomenological Landau-Lifshitz-Gilbert equation of spin dynamics can be rigorously obtained from the Dirac-Kohn-Sham equation and we derive an exact expression for the tensorial Gilbert damping. (ii) We derive, from the gauge-invariant part of the spin-orbit interaction, the existence of a relativistic interaction that linearly couples the angular momentum of the electromagnetic field and the electron spin. We show this spin-photon interaction to provide the previously unknown origin of the angular magneto-electric coupling, to explain coherent ultrafast magnetism, and to lead to a new torque, the optical spin-orbit torque. (iii) We derive a definite description of magnetic inertia (spin nutation) in ultrafast magnetization dynamics and show that it is a higher-order spin-orbit effect. (iv) We develop a unified theory of magnetization dynamics that includes spin currents and show that the nonrelativistic spin currents naturally lead to the current-induced spin-transfer torques, whereas the relativistic spin currents lead to spin-orbit torques. (v) Using the relativistic framework together with ab initio magneto-optical calculations we show that relativistic laser-induced spin-flip transitions do not explain the measured large laser-induced demagnetization. Employing the ab initio relativistic framework, we calculate the amount of magnetization that can be imparted in a material by means of circularly polarized light – the so-called inverse Faraday effect. We show the existence of both spin and orbital induced magnetizations, which surprisingly reveal a different behavior. We establish that the laser-induced magnetization is antisymmetric in the light’s helicity for nonmagnets, antiferromagnets and paramagnets; however, it is only asymmetric for ferromagnets.
12
Burimova, Anastasia. „Spectral and angular distributions of synchrotron radiation in quantum theory“. Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-21032015-220522/.
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In the framework of quantum theory the characteristics of synchrotron radiation (SR) are considered. In order to simplify theoretical description the process of radiation is restricted to single-photon emission. For arbitrary quantum transitions the spectral-angular distributions of SR power are given in exact analytical form. Scalar particles (bosons) and particles with spin $\\hbar/2$ (electrons) are treated separately. Special attention is given to the particular transitions, namely, to the transitions to first excited and ground states. It is shown that the components of linear polarization of radiation from electron switch places due to the orientation of spin when the electron jumps to the ground state. This fact can be considered an analytical proof for the presence of $\\pi$-component of quantum radiation in the plane of motion. The radiation emitted from weakly excited particles is thoroughly analysed. To describe the evolution of the profiles of angular distributions various functions are introduced both for two- and three-level systems. For quantum transitions from the first excited state to the ground state the comparative analysis of radiation from bosons and electrons is performed, which helps to estimate the influence of spin and its direction on the characteristics of radiation. The radiation from unpolarized electron is considered separately. Tracking the behavior of effective angles allows to discover the inconsistency of well-known classical conclusion about the concentration of total (summed over spectrum) ultrarelativistic radiation in the plane of motion. It is shown that the effective angles of quantum radiation tend to finite values and do not vanish in ultrarelativistic region. A brief review of classical theory includes an introduction of the new concept, $n$-part of spectrum. In order to find an adequate classical analogue for the radiation from weakly excited particles, the idea to reduce classical spectrum was developed. It turns out that the characteristics of radiation calculated for reduced classical spectrum stay in good quantitative and qualitative agreement with their quantum analogues, at least for single-harmonic and two-harmonic quantum spectra, and classical theory of a reduced spectrum can be claimed representational in this sense. The evolution of maximum in radiation spectrum is considered in separate chapter. A well-known approximation obtained for critical frequency in the framework of classical theory is invalid when quantum corrections enter the picture. But there appears a possibility to find the conditions for the maximum to shift to the highest harmonic of finite quantum spectrum. It is shown that the shifts occur successively starting with primary harmonic in non-relativistic case, and this result remains valid independently of spin. For a scalar particle there exists a fixed set of numbers, which are the critical values of external field, such that the shift of radiation maximum in the spectrum of boson can only happen when the intensity of external field is greater than certain critical value related to corresponding harmonic. If this condition is not satisfied, the position of maximum remains unchanged. It turns out that the presence of spin perturbs this picture, so that the critical values of field intensity depend on the number of initial level.Consideramos as características da radiação sincrotron (RS) no âmbito da teoria quântica. Para simplificar a descrição teórica do processo de radiação restringimos à consideração da emissão de único fóton. Para transições quânticas arbitrárias, as distribuições espectrais e angulares da potência da RS são dadas de forma analítica exata. Tratamos separadamente partículas escalares (bósons) e com spin ½ (elétrons). Atenção especial é dada às transições particulares, a saber, as transições ao primeiro estado excitado e estado fundamental. É mostrado que os componentes de polarização linear da radiação de elétron se trocam em relação à orientação de spin quando o elétron passa para o estado fundamental. Este fato pode ser considerado como uma comprovação analítica para a presença de -componente da radiação quântica no plano de movimento. Analisamos minuciosamente a radiação emitida pela partícula fracamente excitada. Várias funções são introduzidas para descrever a evolução dos perfis de distribuições angulares para sistemas de dois e três níveis. Para transições quânticas do primeiro estado excitado ao estado fundamental a análise comparativa da radiação de bósons e elétrons é realizada, e isso ajuda à estimar a influência de spin e sua direção sobre as características da RS. A radiação de elétrons não polarizados é considerada separadamente. Observando o comportamento dos ângulos efetivos, é fácil perceber a inconsistência da conclusão clássica bem conhecida sobre a concentração de radiação ultra-relativista total no plano do movimento. Mostramos que os ângulos efetivos da radiação quântica tendem aos valores finitos e não desaparecem na região ultrarelativista. Uma revisão breve da teoria clássica inclui a introdução do conceito novo, isto é a n-parte do espectro. A fim de encontrar um análogo clássico adequado para a radiação das partículas fracamente excitados, a ideia de reduzir o espectro clássico foi desenvolvida. Constatamos que as características da radiação calculadas para o espectro clássico reduzido permanecem em boa concordância, tanto quantitativa quanto qualitativa, com os seus análogos quânticos, pelo menos no que diz respeito aos espectros quânticos de uma ou duas harmônicas. Neste sentido, a teoria clássica do espectro reduzido pode ser chamada de representativa. A evolução do máximo no espectro da radiação é considerada em capítulo separado. A aproximação, comumente considerada na teoria classica para frequência crítica, é inválida quando as correções quânticas entram em cena. Mas existe uma possibilidade de encontrar as condições para o máximo transferir-se à harmônica maior do espectro quântico. É mostrado que as transferências ocorrem sucessivamente, comecando com a harmônica principal no caso não relativístico, e este resultado permanece válido, independentemente de spin. Para uma partícula escalar existe um conjunto fixo dos valores críticos do campo externo, de tal modo que a transferência do máximo da radiação entre duas harmônicas específicas pode acontecer somente quando a intensidade do campo externo é maior do que o valor crítico associado com essas harmônicas. Se essa condição não for satisfeita, a posição do máximo permanece inalterada. Verificamos que a presença de spin perturba esta condição, no caso do elétron os valores críticos da intensidade do campo dependem de número do nível inicial.
13
Stokley, Martin. „An investigation into particle and field ontologies for relativistic scalar fields in de Broglie-Bohm type theories“. Thesis, University of Portsmouth, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343394.
14
Mendonça, Hudson Kazuo Teramoto. „Quebra de supersimetria em 2+1-dimensões“. Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-07082012-173941/.
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Nesse trabalho discutimos alguns aspectos da teoria quântica de campos que nos levam a formulação do potencial efetivo em teorias supersimétricas. O enfoque é dado as técnicas para análise da quebra de supersimetria em 2 + 1-dimensões. São discutidas as condições sobre o potencial efetivo de teorias supersimetrias para que ocorra ou não quebra de supersimetria. O potencial efetivo do modelo Wess-Zumino em 2+1-dimensões é calculado até a aproximação de 2-laços no formalismo de componentes e supercampos e até essa ordem não foi encontrado quebra de supersimetria.In this work we discuss some aspects of quantum theory of fields used for the formulation of the effective potential of supersymmetric theories. The main focus is given to the methods used to analyse supersimmetry breaking in 2 + 1-dimensions. We discuss the conditions on the effective potential of supersymmetric theories for the occurrence of supersymmetry breaking. The effective potential of Wess-Zumino model em 2 + 1-dimensions is calculated up to 2-loops approximation where supersymmetry breaking is not found to this order.
15
Sharkey, Keeper Layne. „Very Accurate Quantum Mechanical Non-Relativistic Spectra Calculations of Small Atoms & Molecules Employing All-Particle Explicitly Correlated Gaussian Basis Functions“. Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/560835.
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Due to the fast increasing capabilities of modern computers it is now feasible to calculate spectra of small atom and molecules with the greater level of accuracy than high-resolution measurements. The mathematical algorithms developed and implemented on high performance supercomputers for the quantum mechanical calculations are directly derived from the first principles of quantum mechanics. The codes developed are primarily used to verify, refine, and predict the energies associated within a given system and given angular momentum state of interest. The Hamiltonian operator used to determine the total energy in the approach presented is called the internal Hamiltonian and is obtained by rigorously separating out the center-of-mass motion (or the elimination of translational motion) from the laboratory-frame Hamiltonian. The methods utilized in the articles presented in this dissertation do not include relativistic corrections and quantum electrodynamic effects, nor do these articles assume the Born-Oppenheimer (BO) approximation with the exception of one publication. There is one major review article included herein which describes the major differences between the non-BO method and the BO approximation using explicitly correlated Gaussian (ECG) basis functions. The physical systems studied in this dissertation are the atomic elements with Z < 7 (although the discussion is not limited to these) and diatomic molecules such as H₂⁺ and H₂ including nuclear isotopic substitution studies with deuterium and tritium, as well as electronic substitutions with the muon particle. Preliminary testing for triatomic molecular functionals using a model potential is also included in this dissertation. It has been concluded that using all-particle ECGs with including the addition of nonzero angular momentum functions to describe nonzero angular momentum states is sufficient in determining the energies of these states for both the atomic and molecular case.
16
Fukuda, Masahiro. „Theoretical Studies of Quantum Electrodynamics for Local Picture of Electron Spin and Time-evolution Simulation Method of Operators“. 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215962.
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Van, Rooy Milton William. „Locating the inner edge of a neutron star crust“. Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5151.
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Thesis (MSc (Physics))--University of Stellenbosch, 2010.ENGLISH ABSTRACT: The overall goal of this project is to study neutron star properties and locate the transition density from the core to the crust using fifteen parameter sets of the effective Skyrme nucleon-nucleon interaction within a method called the dynamical method. Although another approach used to describe nucleon-nucleon interactions called the modified Gogny interaction is briefly discussed in this work, along with a second method for locating the transition density called the thermodynamical method, results using this interaction and method were not generated, but lays some foundation for a PhD project to be undertaken and potentially showing the relation between the interactions and results. The importance of results depends on how well other theoretical approaches to the problem can reproduce those results and to what accuracy. For models to be valid there also has to be good agreement between the theoretical results and known observables. In this project some properties of neutron stars, such as the equation of state, saturation density, binding energy, symmetry energy, slope and incompressibility parameters of symmetry energy are studied. The transition density is located using the dynamical method. Results of the fifteen Skyrme parameter sets show excellent agreement with the published values of the properties of neutron stars and are consistent with their empirical values inferred from nuclear laboratory data, thus validating the use of the Skyrme interactions for describing nuclear matter.
AFRIKAANSE OPSOMMING: Die hoofdoel van hierdie projek is om neutron ster eienskappe te bestudeer en die oorgangsdigtheid vanaf die kors na die kern te vind deur gebruik te maak van vyftien parameter stelle van die effektiewe Skyrme nukleon-nukleon interaksie binne ‘n metode genaamd die dinamiese metode. Alhoewel ‘n ander benadering vir die beskrywing van nukleon-nukleon interaksies, genaamd die gewysigde Gogny interaksie kortliks in hierdie werk beskryf word, asook ‘n tweede metode, genaamd die termodinamiese metode om die oorgangsdigtheid te bepaal, was resultate vir hierdie interaksie en metode nie gegenereer nie, maar l die fondasie vir verdere werk aan ‘n PhD projek wat die verband tussen die twee interaksies en resultate kan wys. Die belangrikheid van resultate hang af van hoe goed ander teoretiese benaderinge tot die problem daardie resultate kan herproduseer en tot watter akkuraatheid. Vir modelle om geldig te wees moet daar ook goeie ooreenkomste wees tussen teoretiese resultate en bekende waarneembare eienskappe. In hierdie projek word sommige eieskappe van neutron sterre, soos die toestandandsvergelyking, versadigingsdigtheid, bindingsenergie, simmetrie-energie, gradiënt en onsaampersbaarheids parameters van die simmetrie-energie bestudeer. Die oorgangsdigtheid word dan gevind deur gebruik te maak van die dinamiese metode. Resultate van die vyftien Skyrme interaksie parameter stelle wys goeie ooreenstemming met die gepubliseerde waardes van die eienskappe van neutron sterre en is konsistent met hulle empiriese waardes afgelei van kern laboratorium data, wat die geldigheid van Skyrme interaksies vir die beskrywing van kernmaterie bevestig.
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Ibnouhsein, Mohamed Issam. „Quantum correlations and causal structures“. Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112426/document.
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Les travaux récents en fondements de la théorie quantique (des champs) et en information quantique relativiste tentent de mieux comprendre les effets des contraintes de causalité imposées aux opérations physiques sur la structure des corrélations quantiques. Le premier chapitre de cette thèse est consacré à l'étude des implications conceptuelles de la non-localité quantique, notion qui englobe celle d'intrication dans un sens précis. Nous détaillons comment les récentes approches informationnelles tentent de saisir la structure des corrélations non-locales, ainsi que les questions que ces dernières soulèvent concernant la capacité d'un observateur localisé à isoler un système de son environnement. Le second chapitre détaille les effets de l'invariance de Poincaré sur la détection et la quantification de l'intrication. Cette invariance impose que tous les systèmes soient modélisés en dernière instance dans le cadre de la théorie des champs, ce qui implique qu'aucun système à énergie finie ne puisse être localisé, ainsi que la divergence de toute mesure d'intrication pour des observateurs localisés. Nous fournissons une solution à ces deux problèmes en démontrant l'équivalence générique qui existe entre une résolution spatiale finie des appareils de mesure et l'exclusion des degrés de liberté de haute énergie de la définition du système observé. Cette équivalence permet une interprétation épistémique du formalisme quantique standard décrivant les systèmes localisés non-relativistes et leurs corrélations, clarifiant ainsi l'origine des mesures finies d'intrication pour de tels systèmes. Le dernier chapitre explore un cadre théorique récemment introduit qui prédit l'existence de corrélations quantiques sans ordre causal défini. Procédant par analogie avec le cas des corrélations non-locales, nous présentons quelques principes informationnels contraignant la structure de ces corrélations dans le but de mieux en comprendre l'origine physiqueRecent works in foundations of quantum (field) theory and relativistic quantum information try to better grasp the interplay between the structure of quantum correlations and the constraints imposed by causality on physical operations. Chapter 1 is dedicated to the study of the conceptual implications of quantum nonlocality, a concept that subsumes that of entanglement in a certain way. We detail the recent information-theoretic approaches to understanding the structure of nonlocal correlations, and the issues the latter raise concerning the ability of local observers to isolate a system from its environment. Chapter 2 reviews in what sense imposing Poincaré invariance affects entanglement detection and quantification procedures. This invariance ultimately forces a description of all quantum systems within the framework of quantum field theory, which leads to the impossibility of localized finite-energy states and to the divergence of all entanglement measures for local observers. We provide a solution to these two problems by showing that there exists a generic equivalence between a finite spatial resolution of the measurement apparatus and the exclusion of high-energy degrees of freedom from the definition of the observed system. This equivalence allows for an epistemic interpretation of the standard quantum formalism describing nonrelativistic localized systems and their correlations, hence a clarification of the origin of the finite measures of entanglement between such systems. Chapter 3 presents a recent theoretical framework that predicts the existence of correlations with indefinite causal order. In analogy to the information-theoretic approaches to nonlocal correlations, we introduce some principles that constrain the structure of such correlations, which is a first step toward a clear understanding of their physical origin
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Sonnenberg, Jason Louis. „Structure and reactivity studies of environmentally relevant actinide-containing species using relativistic density functional theory“. Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1124308219.
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Thesis (Ph. D.)--Ohio State University, 2005.Title from second page of PDF file. Document formatted into pages; contains xxiii, 151 p.; also includes graphics (some col.). Includes bibliographical references (p. 140-151). Available online via OhioLINK's ETD Center
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Lehum, André Carlos. „Quebra de simetria de calibre no modelo de Chern-Simons supersimétrico“. Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-09052008-102010/.
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Através do formalismo de supercampos, estudamos as propriedades ultravioletas da eletrodinâmica quântica supersimétrica no espaço-tempo tridimensional. Mostramos que esta teoria é finita em todas as ordens de perturbação num calibre particular. Também apresentamos uma análise perturbativa do modelo de Chern-Simons supersimétrico acoplado a um supercampo escalar complexo. Com isso, estudamos a quebra da simetria de calibre U(1) e calculamos as primeiras correções quânticas à ação efetiva na fase quebrada. Mostramos que a renormalização da equação de gap é suficiente para assegurar a renormalizabilidade do modelo em um laço de aproximação. Nós também verificamos que quando acoplado a um supercampo escalar sem massa, o modelo de Chern-Simons supersimétrico apresenta geração dinâmica de massa, um mecanismo que em D = 2 + 1 dimensões do espaço-tempo, diferentemente do modelo não-supersimétrico quadridimensional (Coleman- Weinberg), só ocorre a partir da aproximação de dois laços. Alguns outros resultados relacionados são também incluídos nesta tese, tais como um estudo do modelo CP**(N-1) não-comutativo supersimétrico e a equivalência entre os modelos de Maxwell-Chern-Simons e Auto-Dual supersimétricos. Em todo nosso trabalho, supersimetria é manifesta.Within the superfield formalism, we study the ultraviolet properties of the three-dimensional supersymmetric quantum electrodynamics. The theory is shown to be finite at all loops orders in a particular gauge. We also present a perturbative analysis of the supersymmetric Chern-Simons model coupled to a Higgs field. We study the spontaneous symmetry breaking of the U(1) gauge symmetry and evaluate the first quantum corrections to the effective action in the broken phase. We show that the infinite renormalization of the gap equation is enough to ensure the renormalizability of the model at the first loop level. We also verify that when coupled to a massless scalar superfield, the supersymmetric Chern-Simons model present dynamical generation of mass, a mechanism that in D = 2 + 1 spacetime dimensions, differently from the four-dimensional non-supersymetric model (Coleman-Weinberg), only occurs from two-loop order. Some other related results are also enclosed in this thesis, such as a study of the supersymmetric noncommutative CP**(N-1) model and the equivalence between Maxwell-Chern-Simons and Self-Dual supersymmetric models. In whole work, supersymmetry is manifest.
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Lapitski, Denis. „Development of the Quantum Lattice Boltzmann method for simulation of quantum electrodynamics with applications to graphene“. Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:e89cd11b-da2c-4c34-be9f-7b3d711e2e64.
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We investigate the simulations of the the Schrödinger equation using the onedimensional quantum lattice Boltzmann (QLB) scheme and the irregular behaviour of solution. We isolate error due to approximation of the Schrödinger solution with the non-relativistic limit of the Dirac equation and numerical error in solving the Dirac equation. Detailed analysis of the original scheme showed it to be first order accurate. By discretizing the Dirac equation consistently on both sides we derive a second order accurate QLB scheme with the same evolution algorithm as the original and requiring only a one-time unitary transformation of the initial conditions and final output. We show that initializing the scheme in a way that is consistent with the non-relativistic limit supresses the oscillations around the Schrödinger solution. However, we find the QLB scheme better suited to simulation of relativistic quantum systems governed by the Dirac equation and apply it to the Klein paradox. We reproduce the quantum tunnelling results of previous research and show second order convergence to the theoretical wave packet transmission probability. After identifying and correcting the error in the multidimensional extension of the original QLB scheme that produced asymmetric solutions, we expand our second order QLB scheme to multiple dimensions. Next we use the QLB scheme to simulate Klein tunnelling of massless charge carriers in graphene, compare with theoretical solutions and study the dependence of charge transmission on the incidence angle, wave packet and potential barrier shape. To do this we derive a representation of the Dirac-like equation governing charge carriers in graphene for the one-dimensional QLB scheme, and derive a two-dimensional second order graphene QLB scheme for more accurate simulation of wave packets. We demonstrate charge confinement in a graphene device using a configuration of multiple smooth potential barriers, thereby achieving a high ratio of on/off current with potential application in graphene field effect transistors for logic devices. To allow simulation in magnetic or pseudo-magnetic fields created by deformation of graphene, we expand the scheme to include vector potentials. In addition, we derive QLB schemes for bilayer graphene and the non-linear Dirac equation governing Bose-Einstein condensates in hexagonal optical lattices.
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Assirati, João Luis Meloni. „Quantização covariante de sistemas mecânicos“. Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-01072010-130800/.
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Estudamos as restrições impostas pelo princípio da covariância sobre o procedimento de quantização em espaços planos e curvos. Mostramos que o conjunto de todas as quantizações covariantes em espaços planos em coordenadas retangulares é composto de ordenamentos de operadores de posição e momento e exibimos uma parametrização funcional deste conjunto. Deduzimos regras para a quantização covariante em espaços planos em coordenadas gerais. Generalizamos estas quantizações para espaços curvos e mostramos que nestes espaços, além da ambiguidade de ordenamento, surge uma nova ambiguidade relacionada à curvatura. Este novo tipo de ambiguidade explica o surgimento de uma classe grande de potenciais quânticos no problema da quantização de uma partícula não relativística em um espaço curvo.We study the restrictions imposed by the covariance principle on the quantization procedure in flat and curved spaces. We show that the set of all covariant quantizations in flat spaces in rectangular coordinates is composed of position and momentum operator orderings and exhibit a functional parametrization of this set. We deduce rules for the covariant quantization in flat spaces in general coordinates. We generalize these quantizations for curved spaces and show that in such spaces, besides the ordering ambiguity, it appears a new ambiguity related to the curvature. This new kind of ambiguity explains the appearence of a wide class of quantum potentials in the problem of quantization of a non-relativistic particle in curved space.
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Malbouisson, Jorge Mario Carvalho. „Estudo Sobre o Limite Não Relativístico em Teorias de Campos em 2 + 1 Dimensões“. Universidade de São Paulo, 1996. http://www.teses.usp.br/teses/disponiveis/43/43132/tde-24022014-111446/.
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Nesta tese, o limite não re1ativistico em teorias quânticas de campos em 2+1 dimensões é discutido1 perturbativamente, através da introdução de um corte intermediário que permite 0 cálculo de.expansão /P/m das amplitudes quânticas. especificando a origem, no espaço dos estados intermediários, de cada uma. das contribuições. Este procedimento é aplicado à teoria 4 e um esquema de redução a nível das amplitudes, que identifica a contribuição do setor de baixas energias com 0 resultado da teoria não re1ativistica, é proposto. Quando aplicado á teoria de Chern-Simons escalar, este procedimento sugere correlações relativísticas para o espalhamento Aharonov-Bohm.n this thesis, the nonrelativistic limit of quantum field theories in 2 + 1 dimensions is discussed, perturbatively, through the introduction of an intermediate cutoff which generates the /p/m expansion of the quantum amplitudes and specifies the origin of each contribution in the space of the intermediary states. This scheme is applied to the theory 4 and a reduction procedure for the amplitudes that identify the low energy sector contribution with the results of the nonrelativistic theory is proposed. When applied to the scalar Chern-Simons theory, this procedure gives relativistic corrections to the Aharonov- Bohm scattering.
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Lascio, Eduardo Roberto De. „Setor eletrofraco fortemente acoplado na escala TeV: teoria e fenomenologia no LHC“. Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-02052012-101039/.
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Esta tese apresenta estudos sobre uma possível extensão do Modelo Padrão, suas características teóricas e fenomenológicas. São estudados aspectos do Modelo Padrão relevantes para a análise do setor eletrofraco. Motivado pela solução do problema da hierarquia, é introduzido um espaço de cinco dimensões, com a quinta dimensão curva e compactificada em orbifold. Neste espaço são analisados campos escalares, espinoriais e vetoriais, exibindo modos excitados, os chamados modos de Kaluza-Klein. É incluída uma quarta geração de férmions, sendo então possível obter um setor eletrofraco fortemente acoplado na escala TeV, com a condensação de quarks. Este mecanismo é consequência de acoplamentos não universais com o primeiro modo de Kaluza-Klein do glúon, acoplamentos mais intensos com a quarta geração de quarks. É feita a determinação dos parâmetros dos quarks no espaço de cinco dimensões, resultando no setor de quarks do Modelo Padrão como limite da teoria a baixas energias. A análise teórica termina com a determinação dos acoplamentos dos quarks com o primeiro modo de Kaluza-Klein do glúon. Valendo-se da propriedade de o primeiro modo excitado do glúon trocar sabor, mesmo sendo uma partícula neutra, um estudo fenomenológico é realizado, mostrando que é possível observar eventos no LHC que indicam haver o setor fortemente acoplado, mediante a aplicação dos cortes descritos neste trabalho.This thesis presents studies concerning a possible extension of the Standard Model, its theoretical and phenomenological characteristics. Aspects of the Standard Model that are relevant for the analysis of the electroweak sector are studied. In order to solve the hierarchy problem, a space with ve dimensions is introduced, with the fth dimension curved and compactied in orbifold. Within this space scalar, spinorial and vectorial elds are analysed, showing excited modes, the so-called Kaluza-Klein modes. A fourth generation of fermions is included, which makes it possible to obtain a strongly coupled electroweak sector at the TeV scale, with quarks condensation. This mechanism is possible due to non-universal couplings with the rst Kaluza-Klein mode of the gluon, couplings which are stronger with the fourth generation quarks. The quarks parameters in the ve-dimensional space are determined, leading to the quark sector of the Standard Model as a low energy limit of the theory. The theoretical analysis is nished by the determination of the quarks couplings with the rst Kaluza-Klein mode of the gluon. Using the property of avor exchange by the gluon, even this being a neutral particle, a phenomenological study is carried out, showing that is possible to observe events at the LHC that indicate the existence of the strongly coupled sector, by means of the use of the cuts described in this work.
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Henriksson, Johan. „Molecular Quadratic Response Properties with Inclusion of Relativity“. Doctoral thesis, Linköping : Department of Physics, Chemistry and Biology, Linköping University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-11035.
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Sulzer, David. „Modélisation des interactions faibles en théorie de la fonctionnelle de la densité“. Phd thesis, Université de Strasbourg, 2012. http://tel.archives-ouvertes.fr/tel-00945896.
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Les descriptions des interactions faibles et notamment de la dispersion représentent un problème majeur pour la théorie de la fonctionnelle de la densité. En effet, le caractère fortement local des fonctionnelles rend problématique la description des interactions à longue-portée. Aussi, plusieurs stratégies sont envisagées: des corrections des fonctionnelles existantes ou une introduction de méthodes post-Hartree-Fock par séparation de portée. Des résultats dans les deux cas sont exposés. Tout d'abord, la méthodologie hybride est appliquée à des dimères de métaux de transition (Cr2, Mn2 et Zn2). Ensuite, le calcul de coefficients de corrections pour la dispersion dans un cadre relativiste est présenté. Enfin, les interactions faibles peuvent également résulter de l'interaction d'une molécule avec un champ magnétique. Dans ce cadre, une modélisation de la modification de la densité électronique dans les systèmes aromatiques sous l'influence d'un champ magnétique extérieur est présentée.
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Salehi, Kasmaei Babak. „NONEQUILIBRIUM PROBES OF THE QUARK-GLUON PLASMA“. Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1627035862984205.
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Germano, Guilherme Rocha. „Representações irredutíveis unitárias do grupo de Poincaré“. Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-08122016-160042/.
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A teoria de representações de grupos topológicos Hausdorff, localmente compactos e separáveis em espaços de Hilbert separáveis é introduzida, especificada para grupos compactos e comutativos e são obtidas realizações explicitas das representações finitas irredutíveis de $SU(2)$, $SO(3)$, SL(2,C) e $SO(1,3)^{\\uparrow}$. A teoria das representações induzidas é então apresentada e, depois de feita a conexão entre teorias quântico relativísticas livres no espaço plano de Minkowski e representações unitárias irredutíveis de $R^4 times$ SL(2,C), aplicada para obter tais representações e realizar explicitamente os casos correspondentes a partículas elementares com spin definido em espaços que não admitem a definição de operadores de reflexão espacial. A inclusão da operação de reflexão espacial é feita através de uma variação do método das representações induzidas que conduz a representações unitárias {\\bf redutíveis} de $R^4 times$ SL(2,C) para as quais são obtidas equações de onda selecionando espaços irredutíveis, os quais definem partículas elementares admitindo paridade no contexto das teorias quânticas de campos livres.The theory of locally compact, second countable and Hausdorff topological group representations in separable Hilbert spaces is introduced, and specified to compact and commutative groups. Explicit realizations of the finite irreducible representations of $SU(2)$, $SO(3)$, SL(2,C) and $SO(1,3)^{\\uparrow}$ are obtained. The theory of induced representations is then presented and, after the connection between quantum relativistic free theories in flat Minkowski space and unitary irreducible representations of $R^4 times$ SL(2,C) is made, it is applied and used to classify these representations. Explicit realizations of the cases corresponding to elementary particles with definite spin in spaces which do not allow spacial reflection operators are presented. Spacial reflections are carried with a variation of the induced representation method that leads to unitary {\\bf reducible} representations of $R^4 times$ SL(2,C). Wave equations selecting irreducible spaces that define elementary particles admitting parity in quantum free field theories are derived.
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Paquier, Julien. „Théorie de la fonctionnelle de la densité relativiste à séparation de portée“. Thesis, Sorbonne université, 2020. http://www.theses.fr/2020SORUS059.
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Cette thèse de doctorat constitue une contribution à l’extension relativiste de la théorie de la fonctionnelle de la densité à séparation de portée, en combinant un calcul de fonction d’onde relativiste à quatre composantes pour la contribution de longue portée avec une fonctionnelle de la densité relativiste à courte portée complémentaire, basée sur l’Hamiltonien Dirac-Coulomb ou Dirac-Coulomb-Breit sans paire. Nous avons étudié les propriétés du gaz d’électrons homogène relativiste dans l’approximation sans paire pour développer des fonctionnelles de la densité d’échange-corrélation relativistes à courte portée dans l’approximation de la densité locale (LDA). Nous avons implémenté un code de fonctionnelle de la densité relativiste à séparation de portée en tant que module dans le logiciel QUANTUM PACKAGE 2.0 pour tester ces fonctionnelles. Nous avons étendu la fonctionnelle d’échange relativiste à courte portée au niveau de l’approximation du gradient généralisée (GGA). Enfin, nous avons relevé le rôle important de la densité de paire d’échange à coalescence dans l’évaluation correcte de l’énergie d’échange à très courte portéeThis PhD thesis constitutes a contribution to the relativistic extension of the range-separated density functional theory scheme, by combining a relativistic four-component wave function calculation for the long-range contribution with a complementary relativistic short-range exchange-correlation density functional based on the no-pair Dirac-Coulomb or Dirac-Coulomb-Breit Hamiltonian. We have studied properties of the relativistic homogeneous electron gas in the no-pair approximation to develop relativistic short-range exchange-correlation density functionals at the local density approximation (LDA) level. We have implemented a four-component range-separated density functional code as a plugin in the software QUANTUM PACKAGE 2.0 to test these functionals. We have extended the relativistic short-range exchange density functional to the generalized-gradient approximation (GGA) level. Finally, we have pointed out the important role of the on-top exchange pair density in the correct evaluation of the exchange energy at very short-range
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Baldiotti, Mário César. „"Estados quânticos de um elétron em um campo magnético uniforme"“. Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-10062003-015716/.
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Neste trabalho, apresentamos um método que permite explicitar a arbitrariedade contida nas soluções das equações de onda relativísticas, na presença de certos tipos de campos eletromagnéticos externos. Esta arbitrariedade está relacionada com a existência de uma transformação, com a qual podemos reduzir o número de variáveis presentes na equação original. Através desta transformação, criamos uma representação, a qual permite obter novos conjuntos de soluções exatas e construir a função de evolução para a equação de Klein-Gordon. Como resultado, apresentamos novos conjuntos de soluções, estacionárias e não-estacionárias, para o problema em um campo magnético constante e uniforme e a combinação deste campo com um campo elétrico longitudinal.We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation, which reduces effectively the number of variables in the initial equations. Then we use the corresponding representations to construct new sets of exact solutions, which may have a physical interest, and to construct the evolution function to the Klein-Gordon equation. As resulted, we present new sets of stationary and nonstationary solutions in magnetic field and in some superpositions of electric and magnetic fields.
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Taillebois, Emile Raymond Ferreira. „Traço parcial em sistemas relativísticos: uma nova visão“. Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/7484.
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Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq
In this dissertation, the use of the partial trace of momentum degrees of freedom in the construction of spin reduced density matrices for relativistic massive systems is analyzed. In the regime considered here, massive particles can be described by irreducible unitary representations of the Poincar e group, and the base states are labeled by the dynamical variables of momentum and spin. The reduced density matrices obtained by the partial trace of momenta have unusual properties, since they are not covariant under the action of restricted Lorentz transformations. That behavior produces some important consequences in the study of quantum information in relativistic systems. However, recent arguments have been presented against the use of those matrices in the description of processes involving the transfer of information stored in spin degrees of freedom of relativistic massive particles. Those criticisms are discussed in this dissertation and a connection with the structure of the space of states associated with a given unitary representation is established through a detailed study of the induced representation method applied to the Poincar e group. This allows rewriting the criticisms in literature without the need of a speci c model of interaction for the spin measurement. Besides that, the analysis performed here allows to establish a new method to construct e ective spin reduced density matrices. The presented approach allows recovering the results in the literature and, at the same time, to incorporate the criticisms in a consistent way. However, it is necessary to abandon the usual partial trace of the momentum degrees of freedom and the interpretation in the literature for the spin reduced density matrices. The examples presented in the arguments against the usual spin reduced density matrices are studied using the approach proposed in this dissertation.
Nesta dissertação, a utilização do traço parcial dos momentos na construção de matrizes densidade reduzidas de spin para partículas massivas relativisticas é analisada. No regime considerado, as partículas massivas podem ser descritas por representações unitárias do grupo de Poincaré, e os estados de base são rotulados pelas variáveis dinâmicas de momento e spin. As matrizes reduzidas obtidas por meio do traço parcial dos momentos possuem propriedades inusitadas, pois não são covariantes sob a ação de transformações de Lorentz restritas. Essa característica traz consequências importantes para o estudo da teoria da informação quântica em sistemas relativísticos. No entanto, argumentos recentes têm sido apresentados contra o uso dessas matrizes nos processos de transmissões de informação envolvendo os graus de spin de partículas massivas. Essas críticas são discutidas neste trabalho e uma conexão com a estrutura do espaço de estados associado a representação unitária em questão é estabelecida por meio de um estudo detalhado do método das representações induzidas aplicado ao grupo de Poincaré. Isso permite reescrever as críticas presentes na literatura sem a necessidade de se introduzir um modelo específico de interação associado à medida do spin das partículas. Alem disso, a análise realizada nesta dissertação permite estabelecer um novo método para a construção de matrizes densidade reduzidas efetivas de spin. A proposta apresentada permite recuperar os resultados presentes na literatura e, ao mesmo tempo, incorporar as críticas de maneira consistente. No entanto, para isso é necessário abandonar o traço parcial usual dos graus de liberdade de momento e a interpretação dada na literatura para as matrizes densidade reduzidas de spin. Os exemplos apresentados nas argumentações contra as matrizes densidade reduzidas de spin usuais são estudados utilizando o método proposto neste trabalho.
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AL, SALEH-MAHROUSSEH SALOUA. „Calcul relativiste, en electrodynamique quantique, de la diffusion compton sur un electron lie“. Clermont-Ferrand 2, 1988. http://www.theses.fr/1988CLF21098.
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Pour expliquer le deplacement et l'elargissement du pic compton,lorsque l'energie du photon est voisine de l'energie de liaison de l'electron, il est necessaire d'introduire non seulement la liaison et le mouvement de l'electron, mais aussi le recul du mnoyau. On donne un calcul relativiste de la valeur quadratique moyenne de l'impulsion de l'electron et une expression generale des fonctions d'onde radiales. Pour le calcul analytique covariant de l'element de matrice ou utilise un propagateur pour un electron lie dans le schema de furry et determine la secton efficace, sans aucune integration
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Diaz, Alonso Joaquin. „Première partie: analyse quantique relativiste de la matière denseDeuxième partie : quelques problèmes en physique mathématique“. Paris 7, 1985. http://www.theses.fr/1985PA077030.
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Jabbour, Michael. „Bosonic systems in quantum information theory: Gaussian-dilatable channels, passive states, and beyond“. Doctoral thesis, Universite Libre de Bruxelles, 2018. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/272099.
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The symplectic formalism applied to the phase-space representation of bosonic quantum systems provides us with a powerful mathematical tool for the characterisation of Gaussian states and transformations. As a consequence, quantum information protocols involving the latter are very well understood from a theoretical point of view. Nevertheless, it has become clear in recent years that the use of non-Gaussian resources is necessary in order to perform various crucial information-processing tasks. An illustration of this fact can for instance be found in situations where a Gaussian no-go theorem precludes the use of Gaussian transformations in order to achieve a task involving Gaussian states, such as quantum entanglement distillation, quantum error correction, or universal quantum computation. In the first part of this thesis, we develop a new method based on the generating function of a sequence, which gives rise to an elegant description of intrinsically non-Gaussian objects. Building on the generating function of the matrix elements of Gaussian unitaries in Fock basis, our approach gives access to the multi-photon transition probabilities via unexpectedly simple recurrence equations. The method is developed for Gaussian unitaries effecting both passive and active linear coupling between two bosonic modes. It predicts an interferometric suppression term which generalises the Hong-Ou-Mandel effect for more than two indistinguishable photons impinging on a balanced beam splitter. Furthermore, it exhibits an unsuspected 2-photon suppression effect in optical parametric amplification of gain 2, which originates from the indistinguishability between the input and output photon pairs. Finally, we extend our method to Bogoliubov transformations acting on an arbitrary number of modes. In the second part of this thesis, we introduce a class of Gaussian-dilatable bosonic quantum channels (characterised by a Gaussian unitary in their Stinespring dilation) called passive-environment channels. These channels are interesting from a quantum thermodynamical viewpoint because they correspond to the coupling of a bosonic system with a bosonic environment that is passive in the Fock-basis (that is, no energy can be extracted from it by using unitary transformations) followed by discarding the environment. Making use of the generating function, we provide a description of these channels in terms of Gaussian bosonic channels. We then introduce a new preorder relation called Fock-majorization, which coincides with regular majorization for passive states but also induces another relation in terms of mean boson number, thereby connecting the concepts of energy and disorder of a quantum state. We prove various properties of Fock-majorization, showing in particular that the latter can be interpreted as a relation indicating the existence of a heating or amplifying map between two quantum states. This new preorder relation happens to be relevant in the context of passive-environment bosonic channels. Indeed, we show that these channels are Fock-majorization-preserving, so that any two input states that obey a Fock-majorization relation are transformed into output states respecting a similar relation. As a consequence, it also implies that passive-environment channels are majorization-preserving over the set of passive states of the harmonic oscillator. The consequences of majorization preservation are discussed in the context of the so-called entropy photon-number inequality. Most of our results being independent of the specific nature of the system under investigation, they could be generalised to other quantum systems and Hamiltonians, providing new tools that may prove useful in quantum information theory. In the last part of our thesis, we lay out a resource theory of local activity for bosonic systems. We introduce a notion of local-activity distance, and compare it with the work that can be extracted from a quantum state under local unitaries assisted by passive global unitaries. With this framework, we hope to connect the area of continuous-variable bosonic channels together with quantum thermodynamics.Le formalisme symplectique appliqué à la représentation des systèmes bosoniques dans l'espace des phases donne accès à un outil mathématique puissant pour la caractérisation des états gau-ssiens et transformations gaussiennes. Les protocoles d'information quantique impliquant ces derniers sont d'ailleurs très bien compris d'un point de vue théorique. Toutefois, il s'est avéré clair durant ces dernières années que l'utilisation de ressources non-gaussiennes est nécessaire afin d'effectuer des tâches cruciales de traitement de l'information. En effet, certaines tâches — telles que la distillation d’intrication quantique, le codage quantique ou encore le calcul quantique — impliquant des états gaussiens ne peuvent être effectuées avec des transformations gaussiennes. Dans la première partie de cette thèse, nous développons une nouvelle méthode basée sur la fonction génératrice d'une suite qui donne lieu à une description élégante d'objets intrinsèquement non-gaussiens. Se basant sur la fonction génératrice des éléments de matrice d'unitaires gaussiens dans la base de Fock, notre approche donne accès aux probabilités de transition multi-photon via des équations de récurrence étonnamment simples. La méthode est développée pour des unitaires gaussiens produisant des couplages linéaires passifs et actifs entres deux modes bosoniques. Elle prédit un terme d'interférence destructive qui généralise l'effet Hong-Ou-Mandel pour plus de deux photons indistinguables pénétrant dans un diviseur de faisceau équilibré. De plus, elle met en évidence un effet inattendu de suppression de deux photons dans un amplificateur paramétrique optique de gain 2. Cette suppression résulte de l’indistinguabilité entre les paires de photons d’entrée et de sortie. Finalement, nous étendons notre méthode à des transformations de Bogoliubov agissant sur un nombre de modes arbitraire. Dans la seconde partie de cette thèse, nous introduisons une classe de canaux quantiques bosoniques gaussiens-dilatables (caractérisés par un unitaire gaussien dans leur ``Stinespring dilation") appelés canaux à environnement passif. Ces canaux sont intéressants du point de vue de la thermodynamique quantique puisqu’ils correspondent au couplage d’un système bosonique avec un environnement bosonique qui est passif dans la base de Fock (en d’autres termes, il est impossible d’en extraire de l’énergie avec des transformations unitaires), suivi du rejet de l’environnement. Grâce à la fonction génératrice, nous fournissons une description de ces transformations en termes de canaux quantiques bosoniques gaussiens limités par le bruit du vide. Nous introduisons ensuite une nouvelle relation de pré-ordre appelé ``majorization" de Fock, qui coïncide avec la ``majorization" usuelle pour les états passifs mais induit une autre relation en terme du nombre moyen de bosons, connectant ainsi les concepts d’énergie et de désordre d’un état quantique. Dans ce contexte, nous prouvons des propriétés variées de la ``majorization" de Fock et montrons en particulier que cette dernière peut être interprétée comme une relation indiquant l’existence d’une transformation d’amplification entre deux états quantiques. Cette nouvelle relation de pré-ordre s’avère appropriée dans le contexte des canaux bosonique à environnement passif. En effet, nous montrons que ces canaux conservent la ``majorization" de Fock, de sorte que n’importe quels deux états d’entrée obéissant une relation de ``majorization" de Fock sont transformés en états de sortie vérifiant une relation similaire. En particulier, cela implique que les canaux à environnement passif préservent la ``majorization" pour l'ensemble des états passifs de l’oscillateur harmonique. Les conséquences de la préservation de la ``majorization" sont examinées dans le contexte de la ``entropy photon-number inequality". Étant indépendants de la nature spécifique du système étudié, la plupart de nos résultats peuvent être généralisés à d’autres systèmes et hamiltoniens quantiques, donnant lieu à de nouveaux outils qui pourraient s’avérer utiles en théorie de l’information quantique. Dans la dernière partie de notre thèse, nous mettons en place une théorie de l’activité locale pour les système bosoniques. Nous introduisons une notion de distance en terme d'activité locale et la comparons avec le travail qui peut être extrait d'un état quantique avec des unitaires locaux assistés par des unitaires globaux passifs. Le but à long terme est de se baser sur cette théorie afin de connecter les domaines des canaux bosoniques à variables continues et de la thermodynamique quantique.
Doctorat en Sciences de l'ingénieur et technologie
info:eu-repo/semantics/nonPublished
35
Bouvier, Patrick. „Contributions à l’étude de l’effet Hawking pour des modèles en interaction“. Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112356/document.
Annotation:
L'effet Hawking prédit, dans un espace-temps décrivant l'effondrement d'une étoile à symétrie sphérique vers un trou noir de Schwarzschild, qu'un observateur statique, situé à l'infini, observera un flux thermal de particules quantiques à la température de Hawking. La première démonstration mathématique de l'effet Hawking pour des champs quantiques libres est due à Bachelot, dont le travail sur les champs de Klein-Gordon a été ensuite étendu aux champs de Dirac, d'abord par Bachelot lui-même, puis par Melnyk. Ces travaux, placés dans le cadre d'une symétrie sphérique, ont été complétés par Häfner, qui donna une démonstration rigoureuse de l'effet Hawking pour des champs de Dirac, autour d'une étoile s'effondrant vers un trou noir de Kerr. Le but de cette thèse est d'étudier l'effet Hawking non plus dans un modèle de champs quantiques libres, où les problèmes posés se ramènent à l'étude d'équations aux dérivées partielles linéaires, mais dans un modèle de champs de Dirac en interaction. L'interaction est supposée à support compact, statique, et localisée à l'extérieur de l'étoile. Nous choisissons de traiter le cas d'un modèle jouet, dans un espace-temps de dimension 1+1, situation à laquelle on peut se ramener, au moins dans le cas libre, en utilisant la symétrie sphérique du problème. Nous étudions le comportement de champs de fermions de Dirac dans différentes situations : d'abord, pour une observable suivant l'effondrement de l'étoile ; puis pour une observable stationnaire ; enfin, pour une interaction dépendante du temps, localisée près de la surface de l'étoile. Dans chacun de ces cas, nous montrons l'existence de l'effet Hawking et donnons l'état limite correspondantThe Hawking effect predicts that, in a space- time describing the collapse of a spherically symmetric star to a Schwarzschild black hole, a static observer at infinity sees the Unruh state as a thermal state at Hawking temperature. The first mathematical proof of the Hawking effect, in the original setting of Hawking, is due to Bachelot. His work on Klein-Gordon fields has been extended to Dirac fields, in the first place by Bachelot himself, and by Melnyk after that. Those works, placed in the setup of a spherically symmetric star, have been completed by Häfner, who gave a rigorous proof of the Hawking effect for Dirac fields, outside a star collapsing to a Kerr black hole. The aim of this thesis is to study the Hawking effect not for a model of free quantum fields, in which case the problems can be reduced to studies on linear partial differential equations, but for a model of interacting Dirac fields. The interaction will be considered as a static, compactly-supported interaction, living outside the star. We choose to study a toy model in a 1+1 dimensional space-time. Using the fact that the problem is spherically symetric, one can, at least in the free case, reduce the real problem to this toy model. We study the behavior of Dirac fermions fields in various situations : first, for an observable following the star's collapse ; then, for a static observable ; finally, for a time-dependent interaction, fixed close to the star's boundary. In each of those cases, we show the existence of the Hawking Effect and give the corresponding limit state
36
Busch, Xavier. „Effets dispersifs et dissipatifs en théorie quantique des champs en espace-temps courbe pour modéliser des systèmes de matière condensée“. Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112205/document.
Annotation:
Les deux principales prédictions de la théorie quantique des champs en espace-temps courbe, à savoir la radiation de Hawking et la production de paires de particules ayant lieu dans un espace-temps non stationnaire, n'ont jamais été testé expérimentalement et impliquent toutes deux des processus à ultra haute énergie. En conséquence, de telles prédictions doivent être considérées prudemment. En utilisant l'analogie avec des systèmes de matière condensée mise en avant par Unruh, leur analogue pourrait être testé en laboratoire. Par ailleurs, dispersion et dissipation sont toujours présentes dans de tels systèmes, ce qui régularise la théorie à courte distances. Lors d'expériences destinées à tester les prédictions citées ci-dessus, le bruit thermique modifiera le résultat. En effet, il existe une compétition entre l'émission stimulée dudit bruit thermique et l'émission spontanée issue du vide quantique. Afin de mesurer la radiation de Hawking analogue et de l'analogue des productions de paires (souvent appelé effet Casimir dynamique), il est alors nécessaire de calculer les conséquence de la dispersion et de la dissipation, ainsi que d'identifier des observables permettant de certifier que l'amission spontanée a eu lieu. Dans cette thèse, nous analyserons d'abord les effets de la dispersion et de la dissipation à la fois sur la radiation de Hawking et sur la production de paires de particules. Afin d'obtenir des résultats explicites, nous travaillerons avec l'espace-temps de de Sitter. Les symétries de la théorie nous permettront d'obtenir des résultats exacts. Ceux-ci seront alors appliqués aux trous noirs grâce aux ressemblances entre la région proche du trou noir et l'espace de de Sitter. Afin d’introduire de la dissipation, nous considérerons un modèle exactement soluble permettant de modéliser n'importe quel taux de dissipation. Dans un tel modèle, le champ est couplé de manière linéaire à un environnement contenant un ensemble dense de degrés de liberté. Dans un tel contexte, nous étudierons l'intrication des particules produites. Ensuite, nous considérerons des systèmes de matière condensée spécifiques, à savoir les condensats de Bose et les polaritons. Nous analyserons les effets de la dissipation sur l'intrication de l’effet Casimir dynamique. Enfin, nous étudieront de manière générique l'intrication de la radiation de Hawking en présence de dispersion pour des systèmes analoguesThe two main predictions of quantum field theory in curved space-time, namely Hawking radiation and cosmological pair production, have not been directly tested and involve ultra high energy configurations. As a consequence, they should be considered with caution. Using the analogy with condensed matter systems put forward by Unruh, their analogue versions could be tested in the lab. Moreover, the high energy behavior of these systems is known and involved dispersion and dissipation, which regulate the theory at short distances. When considering experiments which aim to test the above predictions, the thermal noise will contaminate the outcome. Indeed, there will be a competition between the stimulated emission from thermal noise and the spontaneous emission out of vacuum. In order to measure the quantum analogue Hawking radiation, or the analogue pair production also called dynamical Casimir effect, one should thus compute the consequences of ultraviolet dispersion and dissipation, and identify observables able to establish that the spontaneous emission took place. In this thesis, we first analyze the effects of dispersion and dissipation on both Hawking radiation and pair particle production. To get explicit results, we work in the context of de Sitter space. Using the extended symmetries of the theory in such a background, exact results are obtained. These are then transposed to the context of black holes using the correspondence between de Sitter space and the black hole near horizon region. To introduce dissipation, we consider an exactly solvable model producing any decay rate. In such a model, the field is linearly coupled to an environment containing a dense set of degrees of freedom. We also study the quantum entanglement of the particles so produced. In a second part, we consider explicit condensed matter systems, namely Bose Einstein condensates and exciton-polariton systems. We analyze the effects of dissipation on entanglement produced by the dynamical Casimir effect. As a final step, we study the entanglement of Hawking radiation in the presence of dispersion for a generic analogue system
37
Dednam, Wynand. „Atomistic simulations of competing influences on electron transport across metal nanocontacts“. Thesis, Universidad de Alicante, 2019. http://hdl.handle.net/10500/26155.
Annotation:
In our pursuit of ever smaller transistors, with greater computational throughput, many
questions arise about how material properties change with size, and how these properties
may be modelled more accurately. Metallic nanocontacts, especially those for which
magnetic properties are important, are of great interest due to their potential spintronic
applications. Yet, serious challenges remain from the standpoint of theoretical and
computational modelling, particularly with respect to the coupling of the spin and lattice
degrees of freedom in ferromagnetic nanocontacts in emerging spintronic technologies. In
this thesis, an extended method is developed, and applied for the first time, to model the
interplay between magnetism and atomic structure in transition metal nanocontacts. The
dynamic evolution of the model contacts emulates the experimental approaches used in
scanning tunnelling microscopy and mechanically controllable break junctions, and is
realised in this work by classical molecular dynamics and, for the first time, spin-lattice
dynamics. The electronic structure of the model contacts is calculated via plane-wave and
local-atomic orbital density functional theory, at the scalar- and vector-relativistic level of
sophistication. The effects of scalar-relativistic and/or spin-orbit coupling on a number of
emergent properties exhibited by transition metal nanocontacts, in experimental
measurements of conductance, are elucidated by non-equilibrium Green’s Function
quantum transport calculations. The impact of relativistic effects during contact formation
in non-magnetic gold is quantified, and it is found that scalar-relativistic effects enhance the force of attraction between gold atoms much more than between between atoms which
do not have significant relativistic effects, such as silver atoms. The role of non-collinear
magnetism in the electronic transport of iron and nickel nanocontacts is clarified, and it is
found that the most-likely conductance values reported for these metals, at first- and lastcontact,
are determined by geometrical factors, such as the degree of covalent bonding in
iron, and the preference of a certain crystallographic orientation in nickel.Physics
Ph. D. (Physics)
38
Ferrer, Philippe Alberto Friedrich. „Approximating the nucleon as a relativistic three particle system“. Thesis, 1996. https://hdl.handle.net/10539/23777.
Annotation:
A dissertation submitted to the faculty of Science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science.
Degree awarded with distinction on 4 December 1996.This dissertation is divided into two parts: the first part deals with the concepts of angular momentum and spin in classical mechanics and quantum mechanics and relativistic quantum mechanics and their connection with magnetic moments. In the second part, a model is set up of a relativistic three particle system, based on the previou.s.ly introduced concepts, which will serve as a template for a nucleon. The spatial component of the Lorentz invariant electrcmagnetic current is computed, and on the basis of it, the magnetic moment in the non-relativistic limit. It will be seen that the ratio -1 for the magnetic moment of the proton to the neutron will be recovered, in accordance 'with the static quark model, static QeD and very close to experiment.
MT2018
39
Emami-Razavi, Mohsen. „Relativistic n-body wave equations in scalar quantum field theory /“. 2006. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR19789.
Annotation:
Thesis (Ph.D.)--York University, 2006. Graduate Programme in Earth and Space Science.Typescript. Includes bibliographical references (leaves 86-90). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR19789
40
Staudte, Donald Stephen. „Spin - 1/2 wave equations in relativistic quantum mechanics“. Phd thesis, 1993. http://hdl.handle.net/1885/109693.
Annotation:
This thesis is concerned with the development of a new spin-1/2 wave equation
in relativistic quantum mechanics. This equation is the spin-1/2 analogue
of the spin-0 Feshbach-Villars equation.
The thesis begins in chapter 1 with a review of the subject of relativistic
wave equations and its place in the development of modern physics. Chapter
2 sees the derivation of the new equation (hereafter referred to as the FV1/2
equation). This derivation is presented at three levels of understanding, and
is combined with an analysis of the equation using elements of the underlying
mathematics of the theories of special relativity and quantum mechanics. The
analysis justifies the methods of derivation of the equation, and its suitability as
a wave equation in relativistic quantum mechanics. It is shown th a t the FV1/2
equation is different to the Dirac equation and other equations in the literature.
One of the striking features of the FV1/2 equation is th a t it contains a less
restrictive dynamics than the conventional Dirac equation. Chapter 3 examines
the solution space and proves some results using the discrete symmetries C,
P and T, which enable a subset of the solution space to be used for physical
applications. It is possible to use a subset of solutions which contain the usual
Dirac negative energy states, or it is possible to use a subset which contains only
positive energy states, but includes states of opposite signs of charge. The second
subset corresponds to the physical properties of particles and antiparticles and
suggests th a t the FV1/2 equation could be useful in atomic physics.
Chapter 4 represents a start on the development of the FV1/2 equation for
use in atomic physics. It contains a study of hydrogenic atoms. The energy
spectra and wavefunctions for hydrogenic atoms are derived using the FV1/2
equation. The method of solution is of comparable difficulty to th a t using the
Dirac equation. The spectra are found to be identical to th a t of the Dirac
equation, but the wavefunctions differ. A calculation of the expectation value of
the Coulomb energy is performed and the results obtained differ from the Dirac
equation results by 6 x 10-3% for Z — 1, and 40% for Z = 70. This suggests
th a t physically measureable quantities should be calculated and compared using
the FV1/2 and Dirac equations. A calculation is presented to show the energy
spectra and wavefunctions obtained are consistent with the literature. The results obtained in this chapter (again) suggest th a t the FV1/2 equation could be useful
for calculations in atomic physics.
Chapter 5 discusses important further work which should be undertaken if
the FV1/2 equation is to become useful to physics. The development in the
previous chapters concentrated on the FV1/2 equation in relativistic quantum
mechanics. It should be also considered as a quantised field equation. The two
electron problem and the calculation of physical quantities are crucial tests of
the FV1/2 equation’s applicability in atomic physics. The mathematical analysis
in chapter 2 can be extended. Suggestions for gaining a deeper mathematical
understanding of the less restrictive dynamics of the FV1/2 equation are given.
Finally some conclusions on what has been achieved in the thesis are presented
in chapter 6.
41
Ruschhaupt, Andreas [Verfasser]. „A relativistic extension of event enhanced quantum theory / von Andreas Ruschhaupt“. 2001. http://d-nb.info/96395864X/34.
42
Wurm, Alexander. „Renormalization group applications in area-preserving nontwist maps and relativistic quantum field theory“. 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3099521.
43
Nyonyi, Yusuf. „Exact solutions for spherical relativistic models“. Thesis, 2011. http://hdl.handle.net/10413/10665.
Annotation:
In this thesis we study relativistic models of gravitating
uids with heat
ow and electric
charge. Firstly, we derive the model of a charged shear-free spherically symmetric cosmological
model with heat
ow. The solution of the Einstein-Maxwell equations of the system
is governed by the pressure isotropy condition. This condition is a highly nonlinear partial
di erential equation. We analyse this master equation using Lie's group theoretic approach.
The Lie symmetry generators that leave the equation invariant are found. We provide exact
solutions to the gravitational potentials using the rst symmetry admitted by the equation.
Our new exact solutions contain the earlier results of Msomi et al (2011) without charge.
Using the second symmetry we are able to reduce the order of the master equation to a rst
order highly nonlinear di erential equation.
Secondly, we study a shear-free spherically symmetric cosmological model with heat
ow
in higher dimensions. We establish the Einstein eld equations and nd the governing
pressure isotropy condition. We use an algorithm due to Deng (1989) to provide several
new classes of solutions to the model. The four-dimensional case is contained in our general
result. Solutions due to Bergmann (1981), Maiti (1982), Modak (1984) and Sanyal and Ray
(1984) for the four-dimensional case are regained. We also establish a new class of solutions
that contains the results of Deng (1989) from four dimensions.Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.
44
Noble, Scott Charles. „A numerical study of relativistic fluid collapse“. Thesis, 2003. http://hdl.handle.net/2152/817.
45
Noble, Scott Charles Morrison Philip J. Choptuik Matthew William. „A numerical study of relativistic fluid collapse“. 2003. http://wwwlib.umi.com/cr/utexas/fullcit?p3122773.
46
Chandra, Nitin. „Topics In Noncommutative Gauge Theories And Deformed Relativistic Theories“. Thesis, 2012. http://etd.iisc.ernet.in/handle/2005/2468.
Annotation:
There is a growing consensus among physicists that the classical notion of spacetime has to be drastically revised in order to nd a consistent formulation of quantum mechanics and gravity. One such nontrivial attempt comprises of replacing functions of continuous spacetime coordinates with functions over noncommutative algebra. Dynamics on such noncommutative spacetimes (noncommutative theories) are of great interest for a variety of reasons among the physicists. Additionally arguments combining quantum uncertain-ties with classical gravity provide an alternative motivation for their study, and it is hoped that these theories can provide a self-consistent deformation of ordinary quantum field theories at small distances, yielding non-locality, or create a framework for finite truncation of quantum field theories while preserving symmetries.
In this thesis we study the gauge theories on noncommutative Moyal space. We nd new static solitons and instantons in terms of the so-called generalized Bose operators (GBO). GBOs are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of GBOs. The Nielsen-Olesen vortex solutions found in terms of these operators also reduce to the ones known in the literature. On the other hand, we nd a class of new instanton solutions which are unitarily inequivalent to the ones found from ADHM construction on noncommutative space. The charge of the instanton has a description in terms of the index representing the reducibility of the Fock space representation, i.e., k. After studying the static soliton solutions in noncommutative Minkowski space and the instanton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also provide an interpretation of our results in the context of non-linear quantum optics. We then shift to the so-called DSR theories which are related to a different kind of noncommutative ( -Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario.
In first chapter we introduce the subjects of the noncommutative quantum theories and the DSR. Chapter 2 starts with describing the GBOs. They correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the GBO. When used in conjunction with the noncommutative ADHM construction, we nd that these new instantons are in general not unitarily equivalent to the ones currently known in literature.
Chapter 3 studies the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative R1;1 perturbatively to linear order in the noncommutativity . We show that the Poisson distribution gets modified, and that the vacuum state evolves into a \squeezed" state rather than a coherent state. The time evolutions of un-certainties in position and momentum in vacuum are also studied and imply interesting consequences for modelling nonlinear phenomena in quantum optics.
In chapter 4 we study thermodynamics of an ideal gas in Doubly Special Relativity. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that DSR thermodynamics is non-perturbative in the SR and massless limits. A stiffer equation of state is found. We conclude our results in the last chapter.
47
Sutanto, Sylvia Hastuti. „Relativistic wave equations, Compton scattering and hydrogenic atoms“. Phd thesis, 2000. http://hdl.handle.net/1885/148028.
48
„The Pauli-Lubanski Vector in a Group-Theoretical Approach to Relativistic Wave Equations“. Doctoral diss., 2016. http://hdl.handle.net/2286/R.I.40221.
Annotation:
abstract: Chapter 1 introduces some key elements of important topics such as; quantum mechanics,
representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´
tivistic wave equations that will play an important role in the work to follow. In Chapter 2,
a complex covariant form of the classical Maxwell’s equations in a moving medium or at
rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum
tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its
connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´
netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.
Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s
equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell
and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´
operators of the Poincare group. A connection between the spin of a particle/field and ´
consistency of the corresponding overdetermined system is emphasized in the massless
case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which
is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨
evolution of exact wave functions of the generalized harmonic oscillators is determined
in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is
shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem
for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the
methods introduced in Chapter 5 a model for the quantization of an electromagnetic field
in a variable media is analyzed. The concept of quantization of an electromagnetic field
in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode
of radiation for this model is used to find time-dependent photon amplitudes in relation
to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the
uncertainty relation, are explicitly given in terms of the Ermakov-type system.Dissertation/Thesis
Doctoral Dissertation Applied Mathematics 2016
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Schumaker, Bonny Laura. „Theoretical Investigations in Nonlinear Quantum Optics, Theory of Measurement, and Pulsations of General Relativistic Models of Neutron Stars“. Thesis, 1985. https://thesis.library.caltech.edu/10414/8/Schumaker_BL_1985.pdf.
Annotation:
This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and moment um variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the ouput modes arise from two-photon transitions, i.e., are created or destroyed two at a time. The states produced by such devices are single-mode and two-mode "squeezed states", special kinds of GPS whose low-noise properties make them attractive for applications in such fields as optical communications and gravitational wave detection. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed as an improved signal-to-noise ratio relative to that obtained with coherent states (the states produced, e.g., by a laser).
The fifth and sixth papers deal with problems of a different nature from that of the previous papers. The fifth paper considers the validity of the "standard quantum limit" (SQL) for measurements which monitor the position of a free mass. It shows specifically that when the pre-measurement wave functions of the free mass and the measuring apparatus(es) are Gaussian (in the general sense, which includes so-called "contractive states"), measurements described by linear couplings to the position or to both the position and momentum are limited by the SQL. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models, and of the gravitational waves they emit.
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Caprez, Adam Preston. „Tests of the Aharonov-Bohm effect“. 2009. http://proquest.umi.com/pqdweb?did=1694329131&sid=4&Fmt=2&clientId=14215&RQT=309&VName=PQD.
Annotation:
Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009.Title from title screen (site viewed June 26, 2009). PDF text: x, 153 p. : ill. (some col.) ; 9 Mb. UMI publication number: AAT 3350442. Includes bibliographical references. Also available in microfilm and microfiche formats.