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Romon, Gabriel. "Contributions to high-dimensional, infinite-dimensional and nonlinear statistics". Electronic Thesis or Diss., Institut polytechnique de Paris, 2023. http://www.theses.fr/2023IPPAG013.
Pełny tekst źródłaThree topics are explored in this thesis: inference in high-dimensional multi-task regression, geometric quantiles in infinite-dimensional Banach spaces and generalized Fréchet means in metric trees. First, we consider a multi-task regression model with a sparsity assumption on the rows of the unknown parameter matrix. Estimation is performed in the high-dimensional regime using the multi-task Lasso estimator. To correct for the bias induced by the penalty, we introduce a new data-driven object that we call the interaction matrix. This tool lets us develop normal and chi-square asymptotic distribution results, from which we obtain confidence intervals and confidence ellipsoids in sparsity regimes that are not covered by the existing literature. Second, we study the geometric quantile, which generalizes the classical univariate quantile to normed spaces. We begin by providing new results on the existence and uniqueness of geometric quantiles. Estimation is then conducted with an approximate M-estimator and we investigate its large-sample properties in infinite dimension. When the population quantile is not uniquely defined, we leverage the theory of variational convergence to obtain asymptotic statements on subsequences in the weak topology. When there is a unique population quantile, we show that the estimator is consistent in the norm topology for a wide range of Banach spaces including every separable uniformly convex space. In separable Hilbert spaces, we establish novel Bahadur-Kiefer representations of the estimator, from which asymptotic normality at the parametric rate follows. Lastly, we consider measures of central tendency for data that lives on a network, which is modeled by a metric tree. The location parameters that we study are called generalized Fréchet means: they obtained by relaxing the square in the definition of the Fréchet mean to an arbitrary convex nondecreasing loss. We develop a notion of directional derivative in the tree, which helps us locate and characterize the minimizers. We examine the statistical properties of the corresponding M-estimator: we extend the notion of stickiness to the setting of metrics trees, and we state a non-asymptotic sticky theorem, as well as a sticky law of large numbers. For the Fréchet median, we develop non-asymptotic concentration bounds and sticky central limit theorems
Razaaly, Nassim. "Rare Event Estimation and Robust Optimization Methods with Application to ORC Turbine Cascade". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLX027.
Pełny tekst źródłaThis thesis aims to formulate innovative Uncertainty Quantification (UQ) methods in both Robust Optimization (RO) and Reliability-Based Design Optimization (RBDO) problems. The targeted application is the optimization of supersonic turbines used in Organic Rankine Cycle (ORC) power systems.Typical energy sources for ORC power systems feature variable heat load and turbine inlet/outlet thermodynamic conditions. The use of organic compounds with a heavy molecular weight typically leads to supersonic turbine configurations featuring supersonic flows and shocks, which grow in relevance in the aforementioned off-design conditions; these features also depend strongly on the local blade shape, which can be influenced by the geometric tolerances of the blade manufacturing. A consensus exists about the necessity to include these uncertainties in the design process, so requiring fast UQ methods and a comprehensive tool for performing shape optimization efficiently.This work is decomposed in two main parts. The first one addresses the problem of rare events estimation, proposing two original methods for failure probability (metaAL-OIS and eAK-MCS) and one for quantile computation (QeAK-MCS). The three methods rely on surrogate-based (Kriging) adaptive strategies, aiming at refining the so-called Limit-State Surface (LSS) directly, unlike Subset Simulation (SS) derived methods. Indeed, the latter consider intermediate threshold associated with intermediate LSSs to be refined. This direct refinement property is of crucial importance since it enables the adaptability of the developed methods for RBDO algorithms. Note that the proposed algorithms are not subject to restrictive assumptions on the LSS (unlike the well-known FORM/SORM), such as the number of failure modes, however need to be formulated in the Standard Space. The eAK-MCS and QeAK-MCS methods are derived from the AK-MCS method and inherit a parallel adaptive sampling based on weighed K-Means. MetaAL-OIS features a more elaborate sequential refinement strategy based on MCMC samples drawn from a quasi-optimal ISD. It additionally proposes the construction of a Gaussian mixture ISD, permitting the accurate estimation of small failure probabilities when a large number of evaluations (several millions) is tractable, as an alternative to SS. The three methods are shown to perform very well for 2D to 8D analytical examples popular in structural reliability literature, some featuring several failure modes, all subject to very small failure probability/quantile level. Accurate estimations are performed in the cases considered using a reasonable number of calls to the performance function.The second part of this work tackles original Robust Optimization (RO) methods applied to the Shape Design of a supersonic ORC Turbine cascade. A comprehensive Uncertainty Quantification (UQ) analysis accounting for operational, fluid parameters and geometric (aleatoric) uncertainties is illustrated, permitting to provide a general overview over the impact of multiple effects and constitutes a preliminary study necessary for RO. Then, several mono-objective RO formulations under a probabilistic constraint are considered in this work, including the minimization of the mean or a high quantile of the Objective Function. A critical assessment of the (Robust) Optimal designs is finally investigated
Jung, Hoon. "Optimal inventory policies for an economic order quantity models under various cost functions /". free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3012983.
Pełny tekst źródłaPolavieja, Gonzalo Garcia de. "Geometric phase and angle for noncyclic adiabatic change, revivals and measures of quantal instability". Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325986.
Pełny tekst źródłaMartins, Andrey Gomes. "\"Evoluções discretas em sistemas quânticos com coordenadas não-comutativas\"". Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-07052007-144956/.
Pełny tekst źródłaWe study the nonrelativistic Quantum Mechanics of physical systems characterized F(Q) X \"A IND.\"teta\"\"(R X \"S POT.1\"), by the presence of an extra degree of freedom which does not commute with the time coordinate. In the language of Noncommutative Geometry, we deal with systems described by an algebra of the form F(Q) X \"A IND.\"teta\"\"(R X \"S POT.1\"),, where F(Q) is the algebra of functions over the usual con¯guration space \"Q\" e \"A IND.\"teta\"\"(R X\"S POT.1\") is a deformation of F(R X \"S POT.1\"), known as noncommutative cylinder. From a geometric viewpoint, the generators of the noncommutative cylinder correspond to the time coordinate and to an extra compact spatial coordinate, just like in Kaluza-Klein theories. We show that because of the noncommutativity between the time coordinate and the extra degree of freedom, the time evolution of systems described by F(Q) X \"A_t(R X S 1) is discretized. We develop the scattering theory for such systems, and verify the presence of a new e®ect: transitions from an in state with energy \"E IND.\"alfa\"\" and an out state with energy \"E IND.\"beta\"\" (diferente de \"E IND.\"alfa\"\") are now allowed, in contrast to the usual case. In fact, transitions take place whenever \"E IND.\"beta\" -\" E IND.\"alfa\" = 2\"pi\"/\"teta\"n,, with n \'PERTENCE A\'. The consequences of this result are investigated in the case of a one-dimensional delta barrier. Our analysis is based on the Born approximation for the transition matrix.
Tilly, David. "Probabilistic treatment planning based on dose coverage : How to quantify and minimize the effects of geometric uncertainties in radiotherapy". Doctoral thesis, Uppsala universitet, Medicinsk strålningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-304180.
Pełny tekst źródłaYang, Kang. "Geometric Aspects in the Hamiltonian Theory of the Fractional Quantum Hall Effect". Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS425.
Pełny tekst źródłaThe topological properties in quantum Hall systems are thoroughly studied in the past thirty years. In constrast, the geometric aspects of quantum Hall systems are far from being fully understood. In this thesis, I am going to investigate the geometric aspects from the view of the composite fermion Hamiltonian theory and test the response of quantum Hall states under anisotropic perturbation. I find in the presence of anisotropy, composite fermions receive mixing effects between different composite fermion Landau levels. A variational metric can be combined to the composite fermions in order to minimize such an effect. The activation gaps and neutral collective gaps are calculated for a quantum Hall system with tilted magnetic field. The former exhibits a robustness while the latter is susceptible to anisotropic perturbation. The charge density wave states under mass anisotropy are also studied. The bubble phase is found to be strongly suppressed by the mass anisotropy. All the first-order phase transitions present in the isotropic case are replaced by continuous phase transitions in the anisotropic case
Javelle, Jérôme. "Cryptographie Quantique : Protocoles et Graphes". Thesis, Grenoble, 2014. http://www.theses.fr/2014GRENM093/document.
Pełny tekst źródłaI want to realize an optimal theoretical model for quantum secret sharing protocols based on graph states. The main parameter of a threshold quantum secret sharing scheme is the size of the largest set of players that can not access the secret. Thus, my goal is to find a collection of protocols for which the value of this parameter is the smallest possible. I also study the links between quantum secret sharing protocols and families of curves in algebraic geometry
Hessmo, Björn. "Quantum optics in constrained geometries". Doctoral thesis, Uppsala University, Department of Quantum Chemistry, 2000. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-1208.
Pełny tekst źródłaWhen light exhibits particle properties, and when matter exhibits wave properties quantum mechanics is needed to describe physical phenomena.
A two-photon source produces nonmaximally entangled photon pairs when the source is small enough to diffract light. It is shown that diffraction degrades the entanglement. Quantum states produced in this way are used to probe the complementarity between path information and interference in Young's double slit experiment.
When two photons have a nonmaximally entangled polarization it is shown that the Pancharatnam phase is dependent on the entanglement in a nontrivial way. This could be used for implementing simple quantum logical circuits.
Magnetic traps are capable of holding cold neutral atoms. It is shown that magnetic traps and guides can be generated by thin wires etched on a surface using standard nanofabrication technology. These atom chips can hold and manipulate atoms located a few microns above the surface with very high accuracy. The potentials are very versatile and allows for highly complex designs, one such design implemented here is a beam splitter for neutral atoms. Interferometry with these confined de Broglie is also considered. These atom chips could be used for implementing quantum logical circuits.
Andreata, Mauro Antonio. "Processos quânticos em cavidades com a geometria variável". Universidade Federal de São Carlos, 2004. https://repositorio.ufscar.br/handle/ufscar/4904.
Pełny tekst źródłaUniversidade Federal de Sao Carlos
In this thesis, we study the quantum de ection of ultracold particles by mirrors, the shrinking of free wave packets, the tunnelling of narrow Gaussian packets through delta potentials and the entanglement between the modes of electromagnetic eld in a vibrating cavity.
Nesta tese, estudamos a de exão quântica de partículas ultrafrias por espelhos, o encolhimento de pacotes de ondas de matéria livres, o tunelamento de estreitos pacotes de ondas gaussianos através de potenciais do tipo delta de Dirac e o emaranhamento entre os modos do campo eletromagnético numa cavidade vibrante.
Couvreur, Romain. "Geometric lattice models and irrational conformal field theories". Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS062.
Pełny tekst źródłaIn this thesis we study several aspects of two-dimensional lattice models of statistical physics with non-unitary features. This bottom-up approach, starting from discrete lattice models, is helpful to understand the features of the associated conformal field theories. They are non-unitary and often irrational, logarithmic or even non-compact. First, we study the problem of the entanglement entropy in non-unitary spin chains and its interpretation in loop models. We discuss the role of the effective central charge, a relevant quantity to study the next problems in this thesis. We then address two problems related to the Chalker-Coddington model, an infinite-dimensional supersymmetric chain important for the study of the plateau transition in the integer quantum Hall effect. Since the model has an infinite number of degrees of freedom, it has been proposed to study it with a series of truncations. We present new results based on this approach and extend this methodology to the case of Brownian motion in its supersymmetric formulation. Next, a new model is proposed to interpolate between class A and class C. The Chalker-Coddington model is a particular realisation of class A whereas class C, describing the physics of the spin quantum Hall effect, can be related to a model of percolation. This interpolating model provides an example of a RG-flow between a non-compact CFT and compact one. The last part of this thesis deals with the problem of classifying observables in lattice models with discrete symmetries. The process is illustrated on the Potts model and its symmetry under the group of permutations and previous results are extended for non-scalar operators. This approach is important to study indecomposability of non-unitary models and can be used to study models such as percolation in higher dimensions
Ari, Wahyoedi Seramika. "La géométrie statistique : une étude sur les cases classique et quantique". Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4033.
Pełny tekst źródłaA fixed theory of gravity is far from being complete. The most promising theory of gravity in this century is general relativity (GR), which is still plagued by several problems. The problems we highlight in this thesis are the thermodynamical aspects and the quantization of gravity. Attempts to understand the termodynamical aspect of GR have already been studied through the thermodynamics of black holes, while the theory of quantum gravity has already had several candidates, one of them being the canonical loop quantum gravity (LQG), which is the base theory in our work
Uranga-Piña, Llinersy. "Ultrafast geometrical rearrangement of solid neon upon photoexcitation of a NO impurity : a quantum dynamics study". Toulouse 3, 2012. http://thesesups.ups-tlse.fr/1904/L.
Pełny tekst źródłaThis thesis reports on results of quantum molecular dynamics simulations of photo-induced structural dynamics in nitric oxide (NO) doped solid neon (Ne). The local perturbation, caused by the optical excitation of the dopant molecule, propagates radially from the NO to the lattice atoms, in a shock-wave-like fashion. The ultrafast relaxation dynamics is studied using a purely quantum mechanical approach, based on a multidimensional shell model, with the shell radii being the dynamical variables. As a consequence of the weak anisotropy of the NO-Ne interaction, the model accounts for the main dynamical features of the rare gas solid while it implies a significant dimensionality reduction with respect to the real condensed phase system. The numerical propagation of the multidimensional wave packet allows the analysis of both the static deformation of the solid due to the impurity and the dynamical response after femtosecond excitation. The photo-induced dynamics of solvent atoms around the impurity centre is found to be a complex collective process, which involves many degrees of freedom. The proposed theoretical methodology allows to consider realistic time-dependent femtosecond pulses and the effect of the pulse duration on the geometrical rearrangement dynamics is clearly shown. The time-resolved absorption spectra were simulated, using the pulse parameters of previous pump-probe spectroscopic experiments, carried out with with femtosecond time-resolution. The computed transient signals qualitatively reproduce the experimental results, thereby enabling a clear analysis of the ultrafast mechanism of the energy transfer into the solid. The influence of explicitly including dynamical correlations in the theoretical treatment of the relaxation dynamics, within the Multi-Configurational Time-Dependent Hartree (MCTDH) scheme, was addressed. This aspect is found to be important only for certain degrees of freedom. The consideration of multi-configurational wave functions does not appreciably modify the values of observables such as the average shell radii, with respect to those obtained employing the time-dependent Hartree ansatz. However, the inclusion of correlations reduces the degree of structuring of the calculated pump-probe signals and improve the agreement with experimental results
Guéré, Jérémy. "Théorie quantique des singularités, symétrie miroir et hiérarchies intégrables". Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066117/document.
Pełny tekst źródłaIn this thesis, we provide a mirror symmetry theorem in a range of cases where the state-of-the-art techniques relying on concavity or convexity do not apply. More specifically, we work on a family of FJRW potentials named after Fan, Jarvis, Ruan, and Witten's quantum singularity theory and viewed as the counterpart of a non-convex Gromov--Witten potential via the physical LG/CY correspondence. The main result provides an explicit formula for Polishchuk and Vaintrob's virtual cycle in genus zero. In the non-concave case of the so-called chain invertible polynomials, it yields a compatibility theorem with the FJRW virtual cycle and a proof of mirror symmetry for FJRW theory. At last, we generalize our main theorem to the computation of intersection numbers between the top Chern class of the Hodge bundle and the virtual cycle in arbitrary genus. In the case of $3$-spin theory, it leads to a proof of Buryak's conjecture on the equivalence between double ramification hierarchy and $3$-KdV hierarchy
Zhang, Mingyi. "Gravité quantique à boucles et géométrie discrète". Thesis, Aix-Marseille, 2014. http://www.theses.fr/2014AIXM4027/document.
Pełny tekst źródłaIn this thesis, I will present how to extract discrete geometries of space-time fromthe covariant formulation of loop quantum gravity (LQG), which is called the spinfoam formalism. LQG is a quantum theory of gravity that non-perturbative quantizesgeneral relativity independent from a fix background. It predicts that the geometryof space is quantized, in which area and volume can only take discrete value. Thekinematical Hilbert space is spanned by Penrose's spin network functions. The excita-tion of geometry can be neatly visualized as fuzzy polyhedra that glued through theirfacets. The spin foam defines the dynamics of LQG by a spin foam amplitude on acellular complex, bounded by the spin network states. There are three main results inthis thesis. First, the semiclassical limit of the spin foam amplitude on an arbitrarysimplicial cellular complex with boundary is studied completely. The classical discretegeometry of space-time is reconstructed and classified by the critical configurations ofthe spin foam amplitude. Second, the three-point function from LQG is calculated.It coincides with the results from discrete gravity. Third, the description of discretegeometries of null hypersurfaces is explored in the context of LQG. In particular, thenull geometry is described by a Euclidean singular structure on the two-dimensionalspacelike surface defined by a foliation of space-time by null hypersurfaces. Its quan-tization is U(1) spin network states which are embedded nontrivially in the unitaryirreducible representations of the Lorentz group
Samson, Edward Carlo Copon. "Generating and Manipulating Quantized Vortices in Highly Oblate Bose-Einstein Condensates". Diss., The University of Arizona, 2012. http://hdl.handle.net/10150/228499.
Pełny tekst źródłaPoulain, Timothé. "On the quantum structure of spacetime and its relation to the quantum theory of fields : k-Poincaré invariant field theories and other examples". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS331/document.
Pełny tekst źródłaAs many theoretical studies point out, the classical description of spacetime, as a continuum, might be no longer adequate to reconcile gravity with quantum mechanics at very high energy (the relevant energy scale being often regarded as the Planck scale). Instead, a more appropriate description could be provided by the data of a noncommutative algebra of coordinate operators replacing the usual commutative local coordinates on smooth manifold. Once the noncommutative nature of spacetime is assumed, it is to expect that the (classical and quantum) properties of field theories on noncommutative background differ from the ones of field theories on classical background. This is the aim of Non-Commutative Field Theory (NCFT) to explore and study these new properties.In the present dissertation, we consider two families of quantum spacetimes of Lie algebra type noncommutativity. The first family is characterised by su(2) noncommutativity and appears in the description of some models of quantum gravity in 3-dimensions. The other family of quantum spacetimes is known in the physics literature as the 4-d kappa-Minkowski space. The importance of this quantum spacetime lies into the fact that its symmetries are provided by the (quantum) kappa-Poincaré algebra (a deformation of the classical Poincaré algebra) together with the fact that the deformation parameter 'kappa', which is of mass dimension, provides a natural energy scale at which the quantum gravity effects may be relevant (and is often regarded as being related to the Planck scale). For these reasons, the kappa-Minkowski space appears as a good candidate for a spacetime to be involved in the description of Doubly Special Relativity and Relative Locality models.To study NCFT it is often convenient to introduce a star product characterising the (noncommutative) C*-algebra of fields modelling the quantum spacetime under consideration. We emphasise that a canonical star product can be obtained by using the group algebraic structures underlying the construction of such Lie algebra type quantum spaces, namely by making use of harmonic analysis on the corresponding Lie group together with the Weyl quantisation scheme. The explicit derivation of such star product for kappa-Minkowski is given. In addition, we show that su(2) Lie algebras of coordinate operators related to quantum spaces with su(2) noncommutativity can be conveniently represented by SO(3)-equivariant poly-differential involutive representations and show that the quantized plane waves obtained from the quantization map action on the usual exponential functions are determined by polar decomposition of operators combined with constraint stemming from the Wigner theorem for SU(2). We finally indicate a convenient way to extend this construction to other semi-simple but non simply connected Lie groups by making use of results from group cohomology with value in an abelian group that would replace the constraints stemming from the simple Wigner theorem.Then, we investigate the quantum properties of various models of interacting scalar field theory on noncommutative background making use of the aforementioned star product formalism to construct physically reasonable expressions for the action functional. Considering quantum spacetime with su(2) noncommutativity, we find that the one-loop 2-point function for complex scalar field theories with quartic interactions is finite, the deformation parameter playing the role of a natural UV cut-off. Special attention is paid to the derivation of the one-loop corrections to both the 2-point and 4-point functions for various models of kappa-Poincaré invariant scalar field theory with quartic interactions. In that case, we show that for some models the 2-point function divergences linearly thus slightly milder than their commutative counterpart, while the one-loop 4-point function is shown to be finite. The results we obtained together with their consequences are finally discussed
Delepouve, Thibault. "Quartic Tensor Models". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS085/document.
Pełny tekst źródłaTensor models are probability measures for random tensors. They generalise matrix models and were developed to study random geometry in arbitrary dimension. Moreover, they are strongly connected to quantum gravity theories as, additionally to the standard bare-bones models, they encompass the field theoretical approach to loop quantum gravity known as group field theory.In the present thesis, we focus on the restricted case of quartic tensor models, for which a far greater number of rigorous mathematical results have been proven. Quartic models can be re-written as multi-matrix models using the intermediate field representation, and their perturbative expansions can be written as series expansions over combinatorial maps. Using a variety of map expansions, we prove analyticity results and useful bounds for the cumulants of various tensor models : the most general standard quartic model at any rank and the simplest renormalisable tensor field theory at rank 3. Then, we introduce a new class of models, the enhanced models, which perturbative expansions display new behaviour, different to the so called melonic behaviour that characterise most known tensor models so far
Christodoulou, Marios. "Transition de géométrie en gravité quantique à boucles covariante". Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0273.
Pełny tekst źródłaIn this manuscript we present a calculation from covariant Loop Quantum Gravity, of a physical observable in a non-perturbative quantum gravitational physical process. The process regards the transition of a trapped region to an anti--trapped region and is treated as a quantum geometry transition akin to gravitational tunneling. The physical observable is the characteristic timescale in which the process takes place. We start with a top--to--bottom formal derivation of the ansatz defining the amplitudes for covariant LQG, starting from the Hilbert-Einstein action. We then take the bottom--to--top path, starting from the EPRL ansatz, to the sum--over--geometries path integral emerging in the semi-classical limit, and discuss its close relation to the naive path integral over the Regge action. We proceed to the construction of wave--packets describing quantum spacelike three-geometries that include a notion of embedding in a Lorentzian spacetime. We derive a simple estimation for the amplitudes describing geometry transition and show that a probabilistic description for such phenomena emerges, with the probability of the phenomena to take place being in general non-vanishing.The Haggard-Rovelli spacetime, modelling the spacetime surrounding the geometry transition region for a black to white hole process, is formulated. We then use the semi--classical approximation to give a general estimation of amplitudes describing the process. We conclude that the transition is predicted to be allowed by LQG, with a crossing time that is linear in the mass. The probability for the process to take place is suppressed but non-zero
Laurent, Philippe. "Méthodes d'accéleration pour la résolution numérique en électrolocation et en chimie quantique". Thesis, Nantes, Ecole des Mines, 2015. http://www.theses.fr/2015EMNA0122/document.
Pełny tekst źródłaThis thesis tackle two different topics.We first design and analyze algorithms related to the electrical sense for applications in robotics. We consider in particular the method of reflections, which allows, like the Schwartz method, to solve linear problems using simpler sub-problems. These ones are obtained by decomposing the boundaries of the original problem. We give proofs of convergence and applications. In order to implement an electrolocation simulator of the direct problem in an autonomous robot, we build a reduced basis method devoted to electrolocation problems. In this way, we obtain algorithms which satisfy the constraints of limited memory and time resources. The second topic is an inverse problem in quantum chemistry. Here, we want to determine some features of a quantum system. To this aim, the system is ligthed by a known and fixed Laser field. In this framework, the data of the inverse problem are the states before and after the Laser lighting. A local existence result is given, together with numerical methods for the solving
Lancien, Cécilia. "High dimension and symmetries in quantum information theory". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSE1077/document.
Pełny tekst źródłaIf a one-phrase summary of the subject of this thesis were required, it would be something like: miscellaneous large (but finite) dimensional phenomena in quantum information theory. That said, it could nonetheless be helpful to briefly elaborate. Starting from the observation that quantum physics unavoidably has to deal with high dimensional objects, basically two routes can be taken: either try and reduce their study to that of lower dimensional ones, or try and understand what kind of universal properties might precisely emerge in this regime. We actually do not choose which of these two attitudes to follow here, and rather oscillate between one and the other. In the first part of this manuscript (Chapters 5 and 6), our aim is to reduce as much as possible the complexity of certain quantum processes, while of course still preserving their essential characteristics. The two types of processes we are interested in are quantum channels and quantum measurements. In both cases, complexity of a transformation is measured by the number of operators needed to describe its action, and proximity of the approximating transformation towards the original one is defined in terms of closeness between the two outputs, whatever the input. We propose universal ways of achieving our quantum channel compression and quantum measurement sparsification goals (based on random constructions) and prove their optimality. Oppositely, the second part of this manuscript (Chapters 7, 8 and 9) is specifically dedicated to the analysis of high dimensional quantum systems and some of their typical features. Stress is put on multipartite systems and on entanglement-related properties of theirs. We essentially establish the following: as the dimensions of the underlying spaces grow, being barely distinguishable by local observers is a generic trait of multipartite quantum states, and being very rough approximations of separability itself is a generic trait of separability relaxations. On the technical side, these statements stem mainly from average estimates for suprema of Gaussian processes, combined with the concentration of measure phenomenon. In the third part of this manuscript (Chapters 10 and 11), we eventually come back to a more dimensionality reduction state of mind. This time though, the strategy is to make use of the symmetries inherent to each particular situation we are looking at in order to derive a problem-dependent simplification. By quantitatively relating permutation symmetry and independence, we are able to show the multiplicative behavior of several quantities showing up in quantum information theory (such as support functions of sets of states, winning probabilities in multi-player non-local games etc.). The main tool we develop for that purpose is an adaptable de Finetti type result
Assemat, Élie. "Sur le rôle des singularités hamiltonniennes dans les systèmes contrôlés : applications en mécanique quantique et en optique non linéaire". Phd thesis, Université de Bourgogne, 2012. http://tel.archives-ouvertes.fr/tel-00833905.
Pełny tekst źródłaLahoche, Vincent. "De la renormalisation perturbative à la renormalisation non-perturbative dans les théories de champ sur groupe à interactions tensorielles". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLS392/document.
Pełny tekst źródłaThis thesis presents a number of tools to deepen our understanding of the underlying physics theories called fields GFTs (Group Field Theories). These theories found their origins in different approaches of quantum gravity, in particular spin foams and random tensors, and are interpreted as quantum space-time or "pre-geometric" models, the amplitudes of Feynman being indexed by triangulations. The understanding of the passage between this "discrete" vision to our continuous space-time remains the great challenge of these theories, for which renormalization, effective theories, research of fixed points and phase transitions proves paramount, and it is the aim of this thesis to understand the tools required for this description. In a first time, we will focus to give a concise description of the perturbative renormalization, and the establishment of a closed system of equations describing exactly the leading order of the theory. Secondly, we will detail the implementation of nonperturbative methods. The functional renormalization group in the first place, providing a first non-perturbative description of these theories, and some nontrivial fixed points. Finally, a constructive approach discussed on two models open the way to a rigorous definition of these theories beyond the perturbative level
Vera-Sorroche, Javier. "Thermal homogeneity and energy efficiency in single screw extrusion of polymers : the use of in-process metrology to quantify the effects of process conditions, polymer rheology, screw geometry and extruder scale on melt temperature and specific energy consumption". Thesis, University of Bradford, 2014. http://hdl.handle.net/10454/13965.
Pełny tekst źródłaDelporte, Nicolas. "Tensor Field Theories : Renormalization and Random Geometry". Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASP011.
Pełny tekst źródłaThis thesis divides into two parts, focusing on the renormalization of quantum field theories. The first part considers three tensor models in three dimensions, a fermionic quartic with tensors of rank-3 and two bosonic sextic, of ranks 3 and 5. We rely upon the large-N melonic expansion of tensor models. For the first model, invariant under U(N)³, we compute the renormalization group flow of the two melonic couplings and establish the vacuum phase diagram, from a reformulation with a diagonalizable matrix intermediate field. Noting a spontaneous symmetry breaking of the discrete chiral symmetry, the comparison with the three-dimensional Gross-Neveu model is made. Beyond the massless U(N)³ symmetric phase, we also observe a massive phase of same symmetry and another where the symmetry breaks into U(N²) x U(N/2) x U(N/2). A matrix model invariant under U(N) x U(N²), sharing the same properties, is also studied.For the two other tensor models, with symmetry groups U(N)³ and O(N)⁵, a non-melonic coupling (the ``wheel") with an optimal scaling in N drives us to a generalized melonic expansion. The kinetic terms are taken of short and long range, and we analyze perturbatively, at large-N, the renormalization group flows of the sextic couplings up to four loops. While the rank-5 model doesn't present any non-trivial fixed point, that of rank 3 displays two real non-trivial Wilson-Fisher fixed points in the short-range case and a line of fixed points in the other. We finally obtain the real conformal dimensions of the primary operators bilinear in the fundamental field.In the second part, we establish the first results of constructive multi-scale renormalization for a quartic scalar field on critical Galton-Watson trees, with a long-range kinetic term. At the critical point, an emergent infinite spine provides a space of effective dimension 4/3 on which to compute averaged correlation fonctions. This approach formalizes the notion of a quantum field theory on a random geometry. We use known probabilistic bounds on the heat-kernel on a random graph. At the end, we sketch the extension of the formalism to fermions and to a compactified spine
Jaffali, Hamza. "Étude de l'Intrication dans les Algorithmes Quantiques : Approche Géométrique et Outils Dérivés". Thesis, Bourgogne Franche-Comté, 2020. http://www.theses.fr/2020UBFCA017.
Pełny tekst źródłaQuantum entanglement is one of the most interesting phenomenon in Quantum Mechanics, and especially in Quantum Information. It is a fundamental resource in Quantum Computing, and its role in the efficiency and accuracy of quantum algorithms or protocols is not yet fully understood. In this thesis, we study quantum entanglement of multipartite states, and more precisely the nature of entanglement involved in quantum algorithms. This study is theoretical, and uses tools mainly coming from algebraic geometry.We focus on Grover’s and Shor’s algorithms, and determine what entanglement classes are reached (or not) by these algorithms, and this is the qualitative part of our study. Moreover, we quantitatively measure entanglement, using geometric and algebraic measures, and study its evolution through the several steps of these algorithms. We also propose original geometrical interpretations of the numerical results.On another hand, we also develop and exploit new tools for measuring, characterizing and classifying quantum entanglement. First, from a mathematical point of view, we study singularities of hypersurfaces associated to quantum states in order to characterize several entanglement classes. Secondly, we propose new candidates for maximally entangled states, especially for symmetric and fermionic systems, using polynomial invariants and geometric measure of entanglement. Finally, we use Machine Learning, more precisely the supervised approach using neural networks, to learn how to recognize algebraic varieties directly related with some entanglement classes
Yang, Ruotao. "Twisted Whittaker category on affine flags and category of representations of mixed quantum group". Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0064.
Pełny tekst źródłaSuppose that G is a reductive group. We have the geometric Satake equivalence which identifies Sph (G), the perverse G (O) equivalent D-modules on affine grassmannin as the category of finite dimensional representation of H, the Langlands dual group of G. We note that: Whit(Gr) = Sph(G). Here, Whit (Gr) is the module category D (N (K), \ chi) -equivalent on Gr. Now, the category of representation admits a deformation by the category of representations of quantum group. On the Whittaker side, we can consider the twisted D-modules on affine grassmannin. This is the fundamental local equivalence: Whit_q (Gr) = Rep_q (H) . Recently, D. Gaitsgory proposed its ramified version. We consider the affine flags instead of the affine grassmannians. In this case, we have to replace the category of quantum group representations with another category, the category of mixed quantum group representations. Whit_q (Fl) = Rep_q ^ {mix} (H) . We prove that the category of twisted Whittaker D-modules on the affine flags and the category of representations of the mixed quantum group are equivalent
Faure, Frédéric. "Approche géométrique de la limite semi-classique par les états cohérents et mécanique quantique sur le tore". Grenoble 1, 1993. http://www.theses.fr/1993GRE10188.
Pełny tekst źródłaCharles, Christoph. "Renormalization and Coarse-graining of Loop Quantum Gravity". Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN053/document.
Pełny tekst źródłaThe continuum limit of loop quantum gravity is still an open problem. Indeed, no proper dynamics in known to start with and we still lack the mathematical tools to study its would-be continuum limit. In the present PhD dissertation, we will investigate some coarse-graining methods that should become helpful in this enterprise. We concentrate on two aspects of the theory's coarse-graining: finding natural large scale observables on one hand and studying how the dynamics of varying graphs could be cast onto fixed graphs on the other hand.To determine large scale observables, we study the case of hyperbolic tetrahedra and their natural description in a language close to loop quantum gravity. The surface holonomies in particular play an important role. This highlights the structure of double spin networks, which consist in a graph and its dual, which seems to also appear in works from Freidel et al. To solve the problem of varying graphs, we consider and define loopy spin networks. They encode the local curvature with loops around an effective vertex and allow to describe different graphs by hidding them in a coarse-graining process. Moreover, their definition gives a natural procedure for coarse-graining allowing to relate different scales.Together, these two results constitute the foundation of a coarse-graining programme for diffeomorphism invariant theories
Collet, François. "Short scale study of 4-simplex assembly with curvature, in euclidean Loop Quantum Gravity". Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4076/document.
Pełny tekst źródłaA study of symmetrical assembly of three euclidean 4-simplices in classical, Regge and quantum geometry. We study the geometric properties and especially the presence of curvature. We show that classical and Regge geometry of the assembly have curvature which evolves in function of its boundary parameters. For the quantum geometry, a euclidean version of EPRL model is used with a convenient value of the Barbero-Immirzi parameter to define the transition amplitude of the assembly and its components. A C++ code is design for compute the amplitudes and study numerically the quantum geometry. We show that a classical geometry, with curvature, emerges already at low spin. We also recognize the appearance of the degenerate configurations and their effects on the expected geometry
Gagatsos, Christos. "Gaussian deterministic and probabilistic transformations of bosonic quantum fields: squeezing and entanglement generation". Doctoral thesis, Universite Libre de Bruxelles, 2014. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209146.
Pełny tekst źródłaThis interplay between phase-space and state-space representations does not represent a particular problem as long as Gaussian states (e.g. coherent, squeezed, or thermal states) and Gaussian operations (e.g. beam splitters or squeezers) are concerned. Indeed, Gaussian states are fully characterized by the first- and second-order moments of mode operators, while Gaussian operations are defined via their actions on these moments. The so-called symplectic formalism can be used to treat all Gaussian transformations on Gaussian states, including mixed states of an arbitrary number of modes, and the entropies of Gaussian states are directly linked to their symplectic eigenvalues.
This thesis is concerned with the Gaussian transformations applied onto arbitrary states of light, in which case the symplectic formalism is unapplicable and this phase-to-state space interplay becomes highly non trivial. A first motivation to consider arbitrary (non-Gaussian) states of light results from various Gaussian no-go theorems in continuous-variable quantum information theory. For instance, universal quantum computing, quantum entanglement concentration, or quantum error correction are known to be impossible when restricted to the Gaussian realm. A second motivation comes from the fact that several fundamental quantities, such as the entanglement of formation of a Gaussian state or the communication capacity of a Gaussian channel, rely on an optimization over all states, including non-Gaussian states even though the considered state or channel is Gaussian. This thesis is therefore devoted to developing new tools in order to compute state-space properties (e.g. entropies) of transformations defined in phase-space or conversely to computing phase-space properties (e.g. mean-field amplitudes) of transformations defined in state space. Remarkably, even some basic questions such as the entanglement generation of optical squeezers or beam splitters were unsolved, which gave us a nice work-bench to investigate this interplay.
In the first part of this thesis (Chapter 3), we considered a recently discovered Gaussian probabilistic transformation called the noiseless optical amplifier. More specifically, this is a process enabling the amplification of a quantum state without introducing noise. As it has long been known, when amplifing a quantum signal, the arising of noise is inevitable due to the unitary evolution that governs quantum mechanics. It was recently realized, however, that one can drop the unitarity of the amplification procedure and trade it for a noiseless, albeit probabilistic (heralded) transformation. The fact that the transformation is probabilistic is mathematically reflected in the fact that it is non trace-preserving. This quantum device has gained much interest during the last years because it can be used to compensate losses in a quantum channel, for entanglement distillation, probabilistic quantum cloning, or quantum error correction. Several experimental demonstrations of this device have already been carried out. Our contribution to this topic has been to derive the action of this device on squeezed states and to prove that it acts quite surprisingly as a universal (phase-insensitive) optical squeezer, conserving the signal-to-noise ratio just as a phase-sensitive optical amplifier but for all quadratures at the same time. This also brought into surface a paradoxical effect, namely that such a device could seemingly lead to instantaneous signaling by circumventing the quantum no-cloning theorem. This paradox was discussed and resolved in our work.
In a second step, the action of the noiseless optical amplifier and it dual operation (i.e. heralded noiseless attenuator) on non-Gaussian states has been examined. We have observed that the mean-field amplitude may decrease in the process of noiseless amplification (or may increase in the process of noiseless attenuation), a very counterintuitive effect that Gaussian states cannot exhibit. This work illustrates the above-mentioned phase-to-state space interplay since these devices are defined as simple filtering operations in state space but inferring their action on phase-space quantities such as the mean-field amplitude is not straightforward. It also illustrates the difficulty of dealing with non-Gaussian states in Gaussian transformations (these noiseless devices are probabilistic but Gaussian). Furthermore, we have exhibited an experimental proposal that could be used to test this counterintuitive feature. The proposed set-up is feasible with current technology and robust against usual inefficiencies that occur in optical experiment.
Noiseless amplification and attenuation represent new important tools, which may offer interesting perspectives in quantum optical communications. Therefore, further understanding of these transformations is both of fundamental interest and important for the development and analysis of protocols exploiting these tools. Our work provides a better understanding of these transformations and reveals that the intuition based on ordinary (deterministic phase-insensitive) amplifiers and losses is not always applicable to the noiseless amplifiers and attenuators.
In the last part of this thesis, we have considered the entropic characterization of some of the most fundamental Gaussian transformations in quantum optics, namely a beam splitter and two-mode squeezer. A beam splitter effects a simple rotation in phase space, while a two-mode squeezer produces a Bogoliubov transformation. Thus, there is a well-known phase-space characterization in terms of symplectic transformations, but the difficulty originates from that one must return to state space in order to access quantum entropies or entanglement. This is again a hard problem, linked to the above-mentioned interplay in the reverse direction this time. As soon as non-Gaussian states are concerned, there is no way of calculating the entropy produced by such Gaussian transformations. We have investigated two novel tools in order to treat non-Gaussian states under Gaussian transformations, namely majorization theory and the replica method.
In Chapter 4, we have started by analyzing the entanglement generated by a beam splitter that is fed with a photon-number state, and have shown that the entanglement monotones can be neatly combined with majorization theory in this context. Majorization theory provides a preorder relation between bipartite pure quantum states, and gives a necessary and sufficient condition for the existence of a deterministic LOCC (local operations and classical communication) transformation from one state to another. We have shown that the state resulting from n photons impinging on a beam splitter majorizes the corresponding state with any larger photon number n’ > n, implying that the entanglement monotonically grows with n, as expected. In contrast, we have proven that such a seemingly simple optical component may have a rather surprising behavior when it comes to majorization theory: it does not necessarily lead to states that obey a majorization relation if one varies the transmittance (moving towards a balanced beam splitter). These results are significant for entanglement manipulation, giving rise in particular to a catalysis effect.
Moving forward, in Chapter 5, we took the step of introducing the replica method in quantum optics, with the goal of achieving an entropic characterization of general Gaussian operations on a bosonic quantum field. The replica method, a tool borrowed from statistical physics, can also be used to calculate the von Neumann entropy and is the last line of defense when the usual definition is not practical, which is often the case in quantum optics since the definition involves calculating the eigenvalues of some (infinite-dimensional) density matrix. With this method, the entropy produced by a two-mode squeezer (or parametric optical amplifier) with non-trivial input states has been studied. As an application, we have determined the entropy generated by amplifying a binary superposition of the vacuum and an arbitrary Fock state, which yields a surprisingly simple, yet unknown analytical expression. Finally, we have turned to the replica method in the context of field theory, and have examined the behavior of a bosonic field with finite temperature when the temperature decreases. To this end, information theoretical tools were used, such as the geometric entropy and the mutual information, and interesting connection between phase transitions and informational quantities were found. More specifically, dividing the field in two spatial regions and calculating the mutual information between these two regions, it turns out that the mutual information is non-differentiable exactly at the critical temperature for the formation of the Bose-Einstein condensate.
The replica method provides a new angle of attack to access quantum entropies in fundamental Gaussian bosonic transformations, that is quadratic interactions between bosonic mode operators such as Bogoliubov transformations. The difficulty of accessing entropies produced when transforming non-Gaussian states is also linked to several currently unproven entropic conjectures on Gaussian optimality in the context of bosonic channels. Notably, determining the capacity of a multiple-access or broadcast Gaussian bosonic channel is pending on being able to access entropies. We anticipate that the replica method may become an invaluable tool in order to reach a complete entropic characterization of Gaussian bosonic transformations, or perhaps even solve some of these pending conjectures on Gaussian bosonic channels.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
Silva, Leonardo Roberto da. "Estudo da geometria da aresta de corte de ferramentas aplicadas ao torneamento de superligas à base de níquel com alta velocidade de corte". Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/18/18135/tde-13052016-153736/.
Pełny tekst źródłaResearchers and industry personnel around the world are firmly committed to the purpose of doing the machining process dramatically faster and more precise. The tough global competition has generated a search for more economical machining processes, with high ability for chip removal and, in this way, producing high quality workpieces. Among the new technologies available nowadays, the high speed machining (HSM) is pointed out as the main solution to obtain competitiveness in a short period of time. The HSM technology appears as an essential component to optimize the efforts for maintaining, and increasing, the global competitiveness. During the last years, high speed machining technology has received great attention, specially the development and availability in the market of machine tools with high rotational speeds (20.000 - 100.000 rpm). The HSM has been used not only to machine aluminum and copper alloys, but also to difficult to machine rnaterials, such as hardened steels and nickel based superalIoys. However, for difficult to machine materiais, the literature is very incipient, specially concerning the turning process. However, before the HSM technology be used in an economic way, alI the components involved in the machining process, including the machine, the spindle, the tool and the operators, need to be tuned with the peculiarities of this new process. Concerning the tooling, they have to satisfy peculiar requirements of safety. Due to the optimization of their geometries, substrates and coatings, the cutting tools are contributing to the success of the process. The present work aims at the study of several insert geometries of ceramic tools (Al2O3 + SiCw and Al2O3 + TiC) and PCBN, with two concentrations of CBN, in the standard format and with modifications on the cutting edge geometry, working in the high speed turning of nickel based superaIloys (lnconel 718 and Waspaloy]. MateriaIs were heat treated to hardness of 44 and 40 HRC, respectively, and machined under dry cutting condition and also with minimal quantity of lubricant (MQL) to attend environmental requirements. The nickel based superalloys are known as difficult to cut materials due to their high hardness, high mechanical strength at high temperature, chemical affinity to tool materiaIs and lower thermal conductivity. The machining of superalloys affects negatively the integrity of the workpiece. For this reason, tool life and surface integrity of the machined component must be carefully analyzed throughout the control of the main machining parameters. Practical experiments were implemented using several cutting conditions and tool geometries to evaluate the following parameters: cutting force, temperature, acoustic emission and surface integrity (surface finishing, residual stress, microhardeness and microstructure) and wear mechanisms. Analyzing the results, the most suitable geometry for the mentioned parameters is recommended and the efficiency of the MQL technical is confirmed. Among all inserts and geometries tested, the CC650 ceramic tool presented better results, followed by the CC670 ceramic tool, both with round format and edge geometry number 2 (chamfer in T 0,15 x 15° with hone of 0,03 mm).
Fontanari, Daniele. "Quantum manifestations of the adiabatic chaos of perturbed susperintegrable Hamiltonian systems". Thesis, Littoral, 2013. http://www.theses.fr/2013DUNK0356/document.
Pełny tekst źródłaThe abundance, among physical models, of perturbations of superintegrable Hamiltonian systems makes the understanding of their long-term dynamics an important research topic. While from the classical standpoint the situation, at least in many important cases, is well understood through the use of Nekhoroshev stability theorem and of the adiabatic invariants theory, in the quantum framework there is, on the contrary, a lack of precise results. The purpose of this thesis is to study a perturbed superintegrable quantum system, obtained from a classical counterpart by means of geometric quantization, in order to highlight the presence of indicators of superintegrability analogues to the ones that characterize the classical system, such as the coexistence of regular motions with chaotic one, due to the effects of resonances, opposed to the regularity in the non resonant regime. The analysis is carried out by studying the Husimi distributions of chosen quantum states, with particular emphasis on stationary states and evolved coherent states. The computation are performed using both numerical methods and perturbative schemes. Although this should be considered a preliminary work, the purpose of which is to lay the fundations for future investigations, the results obtained here give interesting insights into quantum dynamics. For instance, it is shown how classical resonances exert a considerable influence on the spectrum of the quantum system and how it is possible, in the quantum behaviour, to find a trace of the classical adiabatic invariance in the resonance regime
L'abbondanza, fra i modelli fisici, di perturbazioni di sistemi Hamiltoniani superintegrabili rende la comprensione della loro dinamica per tempi lunghi un importante argomento diricerca. Mentre dal punto di vista classico la situazione, perlomeno in molti case importanti, è ben compresa grazie all'uso del teorema di stabilità di Nekhoroshev e della teoria degli invariantiadiabatici, nel caso quantistico vi è, al contrario, una mancanza di risultati precisi. L'obiettivo di questa tesi è di studiare un sistema superintegrabile quantistico, ottenuto partendo da un corrispettivo classico tramite quantizzazione geometrica, al fine di evidenziare la presenza di indicatori di supertintegrabilità analoghi a quelliche caratterizzano il sistema classico, come la coesistenza di moti regolari e caotici, dovuta all'effetto delle risonanze, in contrapposizione con la regolarità nel regime non risonante. L'analisi è condotta studiando le distribuzioni di Husimi di stati quantistici scelti, con particolare enfasi posta sugli stati stazionari e sugli stati coerenti evoluti. I calcoli sono effettuati sia utilizzando tecniche numeriche che schemi perturbativi. Pur essendo da considerardi questo un lavoro preliminare, il cui compito è di porre le fondamenta per analisi future, i risultati qui ottenuti offrono interessanti spunti sulla dinamica quantistica. Per esempio è mostrato come le risonanze classiche abbiano un chiaro effeto sullo spettro del sistema quantistico, ed inoltre comesia possibile trovare una traccia, nel comportamento quantistico, dell'invarianza adiabatica classica nel regime risonante
Pinna, Lorenzo. "On the controllability of the quantum dynamics of closed and open systems". Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLX017/document.
Pełny tekst źródłaWe investigate the controllability of quantum systems in two differentsettings: the standard 'closed' setting, in which a quantum system is seen as isolated, the control problem is formulated on the Schroedinger equation; the open setting that describes a quantum system in interaction with a larger one, of which just qualitative parameters are known, by means of the Lindblad equation on states.In the context of closed systems we focus our attention to an interesting class ofmodels, namely the spin-boson models. The latter describe the interaction between a 2-level quantum system and finitely many distinguished modes of a bosonic field. We discuss two prototypical examples, the Rabi model and the Jaynes-Cummings model, which despite their age are still very popular in several fields of quantum physics. Notably, in the context of cavity Quantum Electro Dynamics (C-QED) they provide an approximate yet accurate description of the dynamics of a 2-level atom in a resonant microwave cavity, as in recent experiments of S. Haroche. We investigate the controllability properties of these models, analyzing two different types of control operators acting on the bosonic part, corresponding -in the application to cavity QED- to an external electric and magnetic field, respectively. We review some recent results and prove the approximate controllability of the Jaynes-Cummings model with these controls. This result is based on a spectral analysis exploiting the non-resonances of the spectrum. As far as the relation between the Rabi andthe Jaynes-Cummings Hamiltonians concerns, we treat the so called rotating waveapproximation in a rigorous framework. We formulate the problem as an adiabaticlimit in which the detuning frequency and the interaction strength parameter goes to zero, known as the weak-coupling regime. We prove that, under certain hypothesis on the ratio between the detuning and the coupling, the Jaynes-Cumming and the Rabi dynamics exhibit the same behaviour, more precisely the evolution operators they generate are close in norm.In the framework of open quantum systems we investigate the controllability ofthe Lindblad equation. We consider a control acting adiabatically on the internal part of the system, which we see as a degree of freedom that can be used to contrast the action of the environment. The adiabatic action of the control is chosen to produce a robust transition. We prove, in the prototype case of a two-level system, that the system approach a set of equilibrium points determined by the environment, i.e. the parameters that specify the Lindblad operator. On that set the system can be adiabatically steered choosing a suitable control. The analysis is based on the application of geometrical singular perturbation methods
Albouy, Olivier. "Discrete algebra and geometry applied to the Pauli group and mutually unbiased bases in quantum information theory". Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00612229.
Pełny tekst źródłaMassuyeau, Gwénaël. "Quelques aspects de la théorie des invariants de type fini en topologie de dimension trois". Habilitation à diriger des recherches, Université de Strasbourg, 2012. http://tel.archives-ouvertes.fr/tel-00734378.
Pełny tekst źródłaLionni, Luca. "Colored discrete spaces : Higher dimensional combinatorial maps and quantum gravity". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS270/document.
Pełny tekst źródłaIn two dimensions, the Euclidean Einstein-Hilbert action, which describes gravity in the absence of matter, can be discretized over random triangulations. In the physical limit of small Newton's constant, only planar triangulations survive. The limit in distribution of planar triangulations - the Brownian map - is a continuum fractal space which importance in the context of two-dimensional quantum gravity has been made more precise over the last years. It is interpreted as a quantum continuum space-time, obtained in the thermodynamical limit from a statistical ensemble of random discrete surfaces. The fractal properties of two-dimensional quantum gravity can therefore be studied from a discrete approach. It is well known that direct higher dimensional generalizations fail to produce appropriate quantum space-times in the continuum limit: the limit in distribution of dimension D>2 triangulations which survive in the limit of small Newton's constant is the continuous random tree, also called branched polymers in physics. However, while in two dimensions, discretizing the Einstein-Hilbert action over random 2p-angulations - discrete surfaces obtained by gluing 2p-gons together - leads to the same conclusions as for triangulations, this is not always the case in higher dimensions, as was discovered recently. Whether new continuum limit arise by considering discrete Einstein-Hilbert theories of more general random discrete spaces in dimension D remains an open question.We study discrete spaces obtained by gluing together elementary building blocks, such as polytopes with triangular facets. Such spaces generalize 2p-angulations in higher dimensions. In the physical limit of small Newton's constant, only discrete spaces which maximize the mean curvature survive. However, identifying them is a task far too difficult in the general case, for which quantities are estimated throughout numerical computations. In order to obtain analytical results, a coloring of (D-1)-cells has been introduced. In any even dimension, we can find families of colored discrete spaces of maximal mean curvature in the universality classes of trees - converging towards the continuous random tree, of planar maps - converging towards the Brownian map, or of proliferating baby universes. However, it is the simple structure of the corresponding building blocks which makes it possible to obtain these results: it is similar to that of one or two dimensional objects and does not render the rich diversity of colored building blocks in dimensions three and higher.This work therefore aims at providing combinatorial tools which would enable a systematic study of the building blocks and of the colored discrete spaces they generate. The main result of this thesis is the derivation of a bijection between colored discrete spaces and colored combinatorial maps, which preserves the information on the local curvature. It makes it possible to use results from combinatorial maps and paves the way to a systematical study of higher dimensional colored discrete spaces. As an application, a number of blocks of small sizes are analyzed, as well as a new infinite family of building blocks. The relation to random tensor models is detailed. Emphasis is given to finding the lowest bound on the number of (D-2)-cells, which is equivalent to determining the correct scaling for the corresponding tensor model. We explain how the bijection can be used to identify the graphs contributing at any given order of the 1/N expansion of the 2n-point functions of the colored SYK model, and apply this to the enumeration of generalized unicellular maps - discrete spaces obtained from a single building block - according to their mean curvature. For any choice of colored building blocks, we show how to rewrite the corresponding discrete Einstein-Hilbert theory as a random matrix model with partial traces, the so-called intermediate field representation
Patureau-Mirand, Bertrand. "Invariants topologiques quantiques non semi-simples". Habilitation à diriger des recherches, Université de Bretagne Sud, 2012. http://tel.archives-ouvertes.fr/tel-00872405.
Pełny tekst źródłaBARACCO, FLAVIO. "HERMANN WEYL AND HIS PHENOMENOLOGICAL RESEARCHES WITHIN INFINITESIMAL GEOMETRY". Doctoral thesis, Università degli Studi di Milano, 2019. http://hdl.handle.net/2434/638166.
Pełny tekst źródłaLe, Floch Yohann. "Théorie spectrale inverse pour les opérateurs de Toeplitz 1D". Phd thesis, Université Rennes 1, 2014. http://tel.archives-ouvertes.fr/tel-01065441.
Pełny tekst źródłaBrunswic, Léo. "Surfaces de Cauchy polyédrales des espaces temps plats singuliers". Thesis, Avignon, 2017. http://www.theses.fr/2017AVIG0420/document.
Pełny tekst źródłaThe study of singular flat spacetimes with polyhedral Cauchy-surfaces is motivated by the quantum gravity toy model role they play in the seminal work of Deser, Jackiw and 'T Hooft. This thesis study parametrisations of classes of singular flat spacetimes : Cauchy-compact maximal flat spacetimes with massive and BTZ-like singularities. Two parametrisations are constructed. The first is based on an extension of Mess theorem to flat spacetimes with BTZ and Penner-Epstein convex hull construction. The second is based on a generalisation of Alexandrov polyhedron theorem to radiant Cauchy-compact flat spacetimes with massive and BTZ-like singularities. This work also initiate a wider theoretical background that encompass singular spacetimes
Yang, Xiaotian. "New transition state optimization and reaction path finding algorithm with reduced internal coordinates". Thesis, Sorbonne université, 2021. http://www.theses.fr/2021SORUS481.
Pełny tekst źródłaThe characteristics of a chemical reaction are largely determined by the molecular structures associated with the reactant, the product, the transition state, and the path connecting them. Therefore, locating the stationary points on the molecular potential surface is the first step towards successful numerical modeling. Mathematically, reactants, products, and reactive intermediates are local minima on the potential energy surface. Two local minima are connected by a stationary point which is a maximum along the reaction path but a minimum in all other directions. This saddle point is called the transition state (TS) between the two local minima. Once all the important stationary points on the potential surface have been located, one can model the whole reaction process, including the mechanism(s) of the reaction and its kinetic and thermodynamic properties (reaction rate, equilibrium constant, exothermicity, etc.. For multistep reactions, the existence of intermediate(s) complicates the reaction mechanism. In addition, there may be multiple possible reaction paths, wherein different intermediate structures connect the same reactants and products. In these complicated scenarios, having a full minimum-energy path showing how reactants and products are connected by various sequences of structures is especially useful, as it provides researchers with atomistic detail about the reaction mechanism. This can be useful, for example, for designing better catalysts. [...]
Cots, Olivier. "Contrôle optimal géométrique : méthodes homotopiques et applications". Phd thesis, Université de Bourgogne, 2012. http://tel.archives-ouvertes.fr/tel-00742927.
Pełny tekst źródłaArchambault, Alexandre. "Optique des ondes de surface : super-résolution et interaction matière-rayonnement". Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00678073.
Pełny tekst źródłaBleu, Olivier. "Physics of quantum fluids in two-dimensional topological systems". Thesis, Université Clermont Auvergne (2017-2020), 2018. http://www.theses.fr/2018CLFAC044/document.
Pełny tekst źródłaThis thesis is dedicated to the description of both single-particle and bosonic quantum fluid Physics in topological systems. After introductory chapters on these subjects, I first discuss single-particle topological phenomena in honeycomb lattices. This allows to compare two theoretical models leading to quantum anomalous Hall effect for electrons and photons and to discuss the photonic quantum valley Hall effect at the interface between opposite staggered cavity lattices.In a second part, I present some phenomena which emerge due to the interplay of the linear topological effects with the presence of interacting bosonic quantum fluid described by mean-field Gross-Pitaevskii equation. First, I show that the spin-anisotropic interactions lead to density-driven topological transitions for elementary excitations of a condensate loaded in the polariton quantum anomalous Hall model (thermal equilibrium and out-of-equilibrium quasi-resonant excitation configurations). Then, I show that the vortex excitations of a scalar condensate in a quantum valley Hall system, contrary to linear wavepackets, can exhibit a robust chiral propagation along the interface, with direction given by their winding in real space, leading to an analog of quantum spin Hall effect for these non-linear excitations. Finally, coming back to linear geometrical effects, I will focus on the anomalous Hall effect exhibited by an accelerated wavepacket in a two-band system. In this context, I present a non-adiabatic correction to the known semiclassical equations of motion which can be expressed in terms of the quantum geometric tensor elements. We also propose a protocol to directly measure the tensor components in radiative photonic systems
Villoutreix, Paul. "Aléatoire et variabilité dans l’embryogenèse animale, une approche multi-échelle". Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015PA05T016/document.
Pełny tekst źródłaWe propose in this thesis to characterize variability quantitatively at various scales during embryogenesis. We use a combination of mathematical models and experimental results. In the first part, we use a small cohort of digital sea urchin embryos to construct a prototypical representation of the cell lineage, which relates individual cell features with embryo-level dynamics. This multi-level data-driven probabilistic model relies on symmetries of the embryo and known cell types, which provide a generic coarse-grained level of observation for distributions of individual cell features. The prototype is defined as the centroid of the cohort in the corresponding statistical manifold. Among several results, we show that intra-individual variability is involved in the reproducibility of the developmental process. In the second part, we consider the mechanisms sources of variability during development and their relations to evolution. Building on experimental results showing variable phenotypic expression and incomplete penetrance in a zebrafish mutant line, we propose a clarification of the various levels of biological variability using a formal analogy with quantum mechanics mathematical framework. Surprisingly, we find a formal analogy between quantum entanglement and Mendel’s idealized scheme of inheritance. In the third part, we study biological organization and its relations to developmental paths. By adapting the tools of algebraic topology, we compute invariants of the network of cellular contacts extracted from confocal microscopy images of epithelia from different species and genetic backgrounds. In particular, we show the influence of individual histories on the spatial distribution of cells in epithelial tissues
Cotfas, Nicolae. "Modèles mathématiques pour cristaux et quasicristauxX". Grenoble INPG, 1998. http://www.theses.fr/1998INPG0130.
Pełny tekst źródłaUsnich, Alexandr. "Sur le groupe de Cremona et ses sous-groupes". Phd thesis, Université Pierre et Marie Curie - Paris VI, 2008. http://tel.archives-ouvertes.fr/tel-00812808.
Pełny tekst źródłaMussard, Bastien. "Modélisation quantochimiques des forces de dispersion de London par la méthode des phases aléatoires (RPA) : développements méthodologiques". Thesis, Université de Lorraine, 2013. http://www.theses.fr/2013LORR0292/document.
Pełny tekst źródłaIn this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of RPA, which is explored in details. We show a summary of a work on the RPA equations with localized orbitals, especially developments of the virtual localized orbitals that are the "projected oscillatory orbitals" (POO). A program has been written to calculate functions such as the exchange hole, the response function, etc... on real space grid (parallelepipedic or of the "DFT" type) ; some of those visualizations are shown here. In the real space, we offer an adaptation of the effective energy denominator approximation (EED), originally developed in the reciprocal space in solid physics. The analytical gradients of the RPA correlation energies in the context of range separation has been derived. The formalism developed here with a Lagrangian allows an all-in-one derivation of the short- and long-range terms that emerge in the expressions of the gradient. These terms show interesting parallels. Geometry optimizations at the RSH-dRPA-I and RSH-SOSEX levels on a set of 16 molecules are shown, as well as calculations and visualizations of correlated densities at the RSH-dRPA-I level
Lee, Cheng-Kuo, i 李正國. "The development of a visual method to quantify geometric characteristic of nano-scale particles". Thesis, 2005. http://ndltd.ncl.edu.tw/handle/2yp79p.
Pełny tekst źródła國立虎尾科技大學
動力機械工程研究所
93
The study successfully developed a visual method to quantify geometric characteristic of nano-scale particles, which combined TEM (Transmission Electron Microscope) and a set of image processing programs. The programs were used to increase the readability of the image of nano-particles obtained by TEM, and to quantify the area, perimeter, equivalent diameter, roundness, shape factor, and compactness of interested objects. The results show that nano-particles are usually non-spherical or of irregular shapes. The theories of the existing instrumentation to measure nano-particles are usually based on the assumption of the spherical particle. Measurements of shape factor, and compactness may be used as correction factors to the errors of such instrumentation to measure nano-particles. These measurements may also be used as indices to represent the irregularity, or to classify the qualities of particles. The study plans to develop a sieving system, with the powder industry, which can narrow down the band of the size distributions of the particles by optimizing the operation parameters.