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Orain, Jean-Christophe. "Frustration géométrique et nouveaux états quantiques de spins dans les composés vanadates fluorés à géométrie kagomé". Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS113/document.
Pełny tekst źródłaThe search for quantum liquid state is a very active field in condensed matter research. In two dimensions, the antiferromagnetic spin 1/2 kagome lattice seems to be the most able to stabilize such a ground state. Indeed, from recent theoretical investigations, we are now quite sure that this model has a quantum spin liquid ground state. However, we still do not know its nature, in particular the nature of its correlations. They could be short ranged with a gap in the excitation spectrum, or long ranged with a gapless excitation spectrum. On the experimental side, only few materials exist and only one possesses a geometrically perfect lattice, the Herbertsmithite. All the experiments that have been done on this compound reveal a gapless spin liquid state along with deviations to the spin 1/2 Heisenberg hamiltonian which could be responsible of the gap closure.This thesis deals with the experimental study, mainly by NMR and µSR, of new vanadium based kagomé compounds which are part of a newly synthesized family, the kagome fluoride vanadates. The material that we studied the most is a spin 1/2 kagomé compound based on V4+, (NH4)2[C7H14N][V7O6F18] (DQVOF). The magnetic model of this compound can be decomposed in two rather independent parts, trimerized kagome planes and quasi paramagnetic V3+ ions. The µSR studies, showing the absence of frozen moment down to 20 mK, reveal a spin liquid ground state in DQVOF. The heat capacity and the NMR experiments point out a gapless behavior despite trimerization and likely weak Dzyaloshinskii Moriya interactions. Our results demonstrate that the gapless ground state, whether intrinsic or due to deviation to the ideal hamiltonian, is a rather robust characteristic of kagome materials.Furthermore, we studied another compound of this family, (NH4)2[C2H8N][V3F12] (DDVF), which magnetic lattice is made of uncoupled kagomé planes based on V3+ (S = 1). The lattice shows large deviations to the ideal kagomé and the thermodynamic experiments and the µSR studies reveal a magnetic transition to a frozen state at 10 K with a long distance order which is effective only below 6 K
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
Girelli, Florian. "Géométrie non commutative et gravité quantique". Aix-Marseille 1, 2002. http://www.theses.fr/2002AIX11039.
Pełny tekst źródłaBaboin, Anne-Céline. "Calcul quantique : algèbre et géométrie projective". Phd thesis, Université de Franche-Comté, 2011. http://tel.archives-ouvertes.fr/tel-00600387.
Pełny tekst źródłaBaboin, Anne-Céline. "Calcul quantique : algèbre et géométrie projective". Electronic Thesis or Diss., Besançon, 2011. http://www.theses.fr/2011BESA2028.
Pełny tekst źródłaThe first vocation of this thesis would be a state of the art on the field of quantum computation, if not exhaustive, simple access (chapters 1, 2 and 3). The original (interesting) part of this treatise consists of two mathematical approaches of quantum computation concerning some quantum systems : the first one is an algebraic nature and utilizes some particular structures : Galois fields and rings (chapter 4), the second one calls to a peculiar geometry, known as projective one (chapter 5). These two approaches were motivated by the theorem of Kochen and Specker and by work of Peres and Mermin which rose from it
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
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
Chaouch, Mohamed. "Contribution à l'estimation non paramétrique des quantiles géométriques et à l'analyse des données fonctionnelles". Phd thesis, Université de Bourgogne, 2008. http://tel.archives-ouvertes.fr/tel-00364538.
Pełny tekst źródłaDjellali, Nadia. "Vers le contrôle géométrique de l'émission de microcavités laser à base de polymères". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2009. http://tel.archives-ouvertes.fr/tel-00516337.
Pełny tekst źródłaNichil, Geoffrey. "Provisionnement en assurance non-vie pour des contrats à maturité longue et à prime unique : application à la réforme Solvabilité 2". Thesis, Université de Lorraine, 2014. http://www.theses.fr/2014LORR0200/document.
Pełny tekst źródłaWe consider an insurance company which has to indemnify a bank against losses related to a borrower defaulting on payments. Models normally used by insurers are collectives and do not allows to take into account the personal characteristics of borrowers. In a first part, we defined a model to evaluate potential future default amounts (provision) over a fixed period.The amount of default is the key to our model. For a borrower j and an associated maturity Tj, this amount is max(Sj Tj -Rj Tj ; 0), where Sj Tj is the outstanding amount owed by the borrower and depends on the borrowed amount and the term of the loan, and Rj Tj is the property sale amount. Rj Tj is proportionate to the borrowed amount; the proportionality coefficient is modeled by a geometric Brownian motion and represents the fluctuation price of real estate. The couples (Maturity of the loan, Term of the loan) are modeled by a Poisson point process. The provision Ph, where h is the maximum duration of the loans, is defined as the sum of the random number of individual defaults amounts. We can calculate the mean and the variance of the provision and also give an algorithm to simulate the provision. It is also possible to estimate the parameters of our model and then give a numerical value of the provision quantile. In the second part we will focus on the solvency need due to provisioning risk (topic imposed by the european Solvency 2 reform). The question will be to study the asymptotic behaviour of Ph when h ! +1. We will show that Ph, well renormalized, converges in law to a random variable which is the sum of two random variables whose one is a Gaussian
Soulé, Paul. "Étude des Bords des Phases de l’Effet Hall Quantique Fractionnaire dans la Géométrie d’un Contact Ponctuel Quantique". Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112215/document.
Pełny tekst źródłaI present in this thesis a study that I did in the university Paris-sud under the supervision of Thierry Jolicœur onto Fractional Quantum Hall (FQH) phases in the cylinder geometry. After a short introduction in the first chapter, I present some basic concept relative to the FQH effect in the second one and introduce some essential features relative to the cylinder geometry, useful for the chapters 3, 4, and 5. The chapter 3 is dedicated to the study of the thin cylinder limit, i.e. when the circumference of the cylinder is of the order of a few magnetic length. In this limit, it is known that the Laughlin wave function at the filling factor 1/q is reduced to a one dimensional crystal in the lowest Landau level orbitals where one every q orbitals is occupied. We Taylor expand the Hamiltonian when the circumference is small compare to the magnetic length in order to study an intermediate limit. When only the first four terms of the development are kept, it is possible to find exact representations of the ground state with "squeezing" operators or matrix products. We also find similar representations for quasiholes, quasielectrons and the magnetorton branch. These results have been published in the article Phys. Rev. B 85, 155116 (2012). In the chapter 4 and 5 I focus onto the gapless chiral edge excitations of FQH phases. I present a microscopic study of those edges states in the cylindrical geometry where quasiparticles are able to tunnel between edges. I first study the principal FQH phase at the filling fraction 1/3 whose ground state is well described by the Laughlin wave function in the chapter 4. For an energy scale lower than the bulk gap, the effective theory is given by a very peculiar one dimensional electron fluid localized at the edge: a chiral Luttinger liquid. Using numerical exact diagonalizations, we study the spectrum of edge modes formed by the two counter-propagating edges on each side of the cylinder. We show that the two edges combine to form a non-chiral Luttinger liquid, where the current term reflects the transfer of quasiparticles between edges. This allows us to estimate numerically the Luttinger parameter for a small number of particles and find it coherent with the one predicted by X. G. Wen theory. We published this work in Phys. Rev. B 86, 115214 (2012). I then analyze edge modes of the FQH phase at filling fraction 5/2 in the chapter 5. From a Conformal Field Theory (CFT) based construction, Moore and Read (Nucl. Phys. B, 1991) proposed that the essential physics of this phase is described by a paired state of composite fermions. A striking property of this state is that emergent excitations braid with non-Abelian statistics. When localized along the edge, those excitations are described through a chiral boson and a Majorana fermion. In the cylinder geometry, we show that the spectrum of edge excitations is composed of all conformal towers of the IsingxU(1) model. In addition, with a Monte Carlo method, we estimate the various scaling dimensions for large systems (about 50 electrons), and find them consistent with the CFT predictions.In the last chapter of my manuscript, I present a work that I did in UBC (Vancouver) in collaboration with Marcel Franz onto quantum spin Hall phases in graphene induced by adatoms. In this system, adatoms induce a spin orbit coupling for electrons in the graphene sheet and create some disorder which might be responsible for destruction the spectral gap. We show in this chapter and in the article [Phys. Rev. B 89, 201410(R) (2014)] that the spectral gap remains open for a realistic range of parameters. In addition, with analytical computations in the low energy approximation and numerical exact diagonalizations, we find characteristic signal in the local density of states highlighting the presence of topological gap. This signal might be observed in scanning tunneling spectroscopy experiments
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
Pereira, Roberto. "Géométrie des simplexes et modèles de mousses de spin". Thesis, Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX22024/document.
Pełny tekst źródłaIn this thesis we present a construction of the quantum amplitude associated to a Lorentzian 4-simplex, modifying a previous construction by Barrett and Crane. This 4-simplex amplitude is further used to construct a path integral defining a sum over simplicial geometries for a fixed triangulation of space-time. As a result we obtain a boundary state space given by spin-networks, establishing a connection between spin foams and Loop Quantum Gravity. Finally, we perform the semiclassical analysis for a single order is given by the exponential af the Regge action
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
Krajewski, Thomas. "Géométrie non commutative et intéractions fondamentales". Aix-Marseille 1, 1998. http://www.theses.fr/1998AIX11072.
Pełny tekst źródłaFaure, 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 źródłaMartinetti, Pierre. "Distances en géométrie non commutative". Aix-Marseille 1, 2001. http://www.theses.fr/2001AIX11032.
Pełny tekst źródłaCette thèse étudie l'aspect métrique de la géométrie non commutative à travers la formulation de Connes de la distance entre états d'une algèbre. La définition d'un espace non commutatif est l'objet du premier chapitre. Des propriétés générales de la formule de la distance sont mises en évidence ainsi que d'importantes simplifications quand l'algèbre est de von Neumann. Dans le deuxième chapitre, les distances sont calculées pour des algèbres de dimension finie. Les cas "Cn" et "Mn(C)" sont envisagés. Dans le troisième chapitre, on étudie la distance pour des géométries obtenues par produit de l'espace-temps riemannien avec une géométrie discrète. Des conditions sont établies garantissant que l'espace discret soit orthogonal, au sens du théorème de Pythagore, à l'espace continu. On obtient ainsi une description complète de la métrique pour un exemple de base de la géométrie non commutative, le modèle à deux couches. On montre également en toute généralité que la métrique d'une géométrie n'est pas perturbée quand on réalise son produit avec une autre géométrie. Le dernier chapitre étudie l'évolution de la métrique lorsque la géométrie est perturbée par des champs de jauges. En se limitant à la partie scalaire de ces champs, on calcule les distances dans la géométrie du modèle standard. Il apparaît que le champ de Higgs est le coefficient d'une métrique riemannienne dans un espace de dimension 4 (continues) + 1 (discrète)
Cots, Olivier. "Contrôle optimal géométrique : méthodes homotopiques et applications". Phd thesis, Université de Bourgogne, 2012. http://tel.archives-ouvertes.fr/tel-00742927.
Pełny tekst źródłaCardona, Alexander. "Géométrie de familles de complexes elliptiques, dualité et anomalies". Clermont-Ferrand 2, 2002. http://www.theses.fr/2002CLF22358.
Pełny tekst źródłaBouddou, Ali. "Détermination de la structure géométrique précise des petites molécules par combinaison de méthodes expérimentales, ab initio et empiriques". Lille 1, 1998. https://pepite-depot.univ-lille.fr/LIBRE/Th_Num/1998/50376-1998-257.pdf.
Pełny tekst źródłaMalik, Nitin singh. "Les fils photoniques : une géométrie innovante pour la réalisation de sources de lumière quantique brillantes". Phd thesis, Université de Grenoble, 2011. http://tel.archives-ouvertes.fr/tel-00681846.
Pełny tekst źródłaMalik, Nitin Singh. "Les fils photoniques : une géométrie innovante pour la réalisation de sources de lumière quantique brillantes". Thesis, Grenoble, 2011. http://www.theses.fr/2011GRENY069/document.
Pełny tekst źródłaThis thesis presents the realization of an efficient single-photon source based on an InAs quantum dot integrated in a photonic nanowire. A photonic nanowire is a monomode waveguide made of a high refractive index material (GaAs in our case). For an optimal wire diameter around 200 nm, nearly all the spontaneous emission of the embedded single-photon emitter (free space wavelength 950 nm) is funnelled into the fundamental guided mode. In addition, the outcoupling efficiency of the guided photon to a microscope objective can be brought close to one with a proper engineering of the wire ends. The source thus features an integrated bottom mirror and a smooth tapering of the wire upper end. High performances are maintained over a broad wavelength range, a key asset of this 1D photonic structure. This thesis presents the physics which governs these structures, their realization, and their characterization. Under pulsed optical pumping, we demonstrate a single-photon source with a record efficiency of 0.72, combined with highly pure single-photon emission. We also discuss the possibility to obtain polarization control, using wire with an elliptical section
De, Goursac Axel. "Géométrie non-commutative, théorie de jauge et renormalisation". Phd thesis, Université Paris Sud - Paris XI, 2009. http://tel.archives-ouvertes.fr/tel-00498767.
Pełny tekst źródłaBen, Yahia Hamed. "Intégralité classique et quantique de quelques systèmes dynamiques". Paris 7, 2008. http://www.theses.fr/2008PA077048.
Pełny tekst źródłaThis thesis is devoted to the study of the integrability of some dynamical Systems. In a first job, we've got a new family (enumerable) of integrable Systems on the sphere S ^2 wich genralizes the Neumann System. In a second job, on metrics called muticenter with integrable géodésie flow, we've show that they do belong to the Bianchi A metrics. Among them, those for Bianchi Vl_0 and Vll_0 seemed to be non-diagonal, but we've prove that in those two cases, apropriates coordinates changes allow to diagonalize them. Finally, for the Bianchi II metric we have highlighted the existence, in classical level, of a new W-algebra for conserved observables. Those two works, have been published in journals, but we've include in the thesis, two other works for which we have not obtain general solutions and that will lead to publications. -Construction of multi-center metrics in the Bianchi B classes. -Construction, in dimension 2, of all Stäckel Systems that do have an extra conserved quadratic quatity. In the first case we have been able to solve the problem for Bianchi B III, and for the second we have only been able to get particular solutions
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
Viennot, David. "Géométrie et adiabaticité des systèmes photodynamiques quantiques". Phd thesis, Université de Franche-Comté, 2005. http://tel.archives-ouvertes.fr/tel-00011145.
Pełny tekst źródłaMourad, Jihad. "Localisation relativiste, mécanique quantique relativiste à deux fermions, géométrie non commutative et théories de Kaluza-Klein". Paris 11, 1994. http://www.theses.fr/1994PA112139.
Pełny tekst źródłaBonzom, Valentin. "Géométrie quantique dans les mousses de Spins : de la théorie topologique BF vers la relativité générale". Thesis, Aix-Marseille 2, 2010. http://www.theses.fr/2010AIX22072/document.
Pełny tekst źródłaLoop quantum gravity has provided us with a canonical framework especially devised for back-ground independent and diffeomorphism invariant gauge field theories. In this quantization the funda-mental excitations are called spin network states, and in the context of general relativity, they give ameaning to quantum geometry. Spin foams are a sort of path integral for spin network states, supposed to enable the computations of transition amplitudes between these states. The spin foam quantization has proved very efficient for topological field theories, like 2d Yang-Mills, 3d gravity or BF theories. Different models have also been proposed for 4-dimensional quantum gravity.In this PhD manuscript, I discuss several methods to study spin foam models. In particular, I present some recurrence relations on spin foam amplitudes, which generically encode classical symme-tries at the quantum level, and are likely to help fill the gap with the Hamiltonian constraints. These relations can be naturally interpreted in terms of elementary deformations of discrete geometric struc-tures, like simplicial geometries. Another interesting method consists in exploring the way spin foam models can be written as path integrals for systems of geometries on a lattice, taking inspiration from topological models and Regge calculus. This leads to a very geometric view on spin foams, and gives classical action principles which are studied in details
Akueson, Anani. "Eléments de géométrie tressée". Valenciennes, 1998. https://ged.uphf.fr/nuxeo/site/esupversions/2b3a587c-d83e-4d2a-96f1-a05576bb88fb.
Pełny tekst źródłaJavelle, 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
Marcillaud, de Goursac Axel. "Géométrie non-commutativeThéorie de jauge et renormalisation". Paris 11, 2009. http://www.theses.fr/2009PA112059.
Pełny tekst źródłaNowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on “noncommutative spaces” are indeed much investigated, and suffer from a new type of divergence called the ultraviolet-infrared mixing. However, this problem has recently been solved by H. Grosse and R. Wulkenhaar by adding to the action of a noncommutative scalar model an harmonic trem, which renders it renormalizable. The aim of this thesis is the extension of this procedure to gauge theories on the Moyal space. Indeed, we have introduced a new noncommutative gauge theory, strongly related to the Grosse-Wulkenhaar model, and candidate to renormalizability. We have then studied the most important properties of this action, and in particular its vacuum configurations. Finally, we give a mathematical interpretation of this new action in terms of a derivation-based differential calculus associated to a superalgebra
Harrivel, Ramiaramanana Dikanaina. "Théorie des champs : approche multisymplectique de la quantification, théorie perturbative et application". Angers, 2005. http://www.theses.fr/2005ANGE0027.
Pełny tekst źródłaThe main subject of this thesis is the study of the Klein-Gordon equation together with an interaction term and the quantization of this theory from the multisymplectic point of view. Multisymplectic geometry provides a general framework for a covariant finite dimensional Hamiltonian formulation of variational problems with several variables. In the first part we study the linear Klein-Gordon equation (free fields). We propose a description of the canonical quantization of free fiels from the multisymplectic point of view. We investigate three approachs : the algebraic approach by giving a representation of the Lie algebra of the symetries, the deformation point of view and finally we introduce a notion of multisymplectic geometric quantization. In the second part we study the classical Øp-theory. First we define explicitely a conserved quantity using a perturbative expansion based on planar trees and a kind of Feynman rule. Then we link this expansion with Butcher series which describe the perturbative expansion of the solutions of some PDE and we show how Butcher series can be related to perturbative quantum theory. Finally we see how we can apply our result in order to solve problems from control theory
Albouy, Olivier. "Algèbre et géométrie discrètes appliquées au groupe de Pauli et aux bases décorrélées en théorie de l'information quantique". Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00402290.
Pełny tekst źródłaPuis nous étudions de façon systématique la possibilité de construire de telles bases au moyen des opérateurs de Pauli. 1) L'étude de la droite projective sur (Z_d)^m montre que, pour obtenir des ensembles maximaux de bases décorrélées à l'aide d'opérateurs de Pauli, il est nécessaire de considérer des produits tensoriels de ces opérateurs. 2) Les sous-modules lagrangiens de (Z_d)^2n, dont nous donnons une classification complète, rendent compte des ensembles maximalement commutant d'opérateurs de Pauli. Cette classification permet de savoir lesquels de ces ensembles sont susceptibles de donner des bases décorrélées : ils correspondent aux demi-modules lagrangiens, qui s'interprètent encore comme les points isotropes de la droite projective (P(Mat(n, Z_d)^2),ω). Nous explicitons alors un isomorphisme entre les bases décorrélées ainsi obtenues et les demi-modules lagrangiens distants, ce qui précise aussi la correspondance entre sommes de Gauss et bases décorrélées. 3) Des corollaires sur le groupe de Clifford et l'espace des phases discret sont alors développés.
Enfin, nous présentons quelques outils inspirés de l'étude précédente. Nous traitons ainsi du rapport anharmonique sur la sphère de Bloch, de géométrie projective en dimension supérieure, des opérateurs de Pauli continus et nous comparons l'entropie de von Neumann à une mesure de l'intrication par calcul d'un déterminant.
CHAU, Huu-Tai. "Symétrie et géométrie du problème à N-corps. Application à la physique nucléaire". Phd thesis, Université de Caen, 2002. http://tel.archives-ouvertes.fr/tel-00002252.
Pełny tekst źródłaLefrançois, Matthieu. "Théorie des champs topologiques et mécanique quantique en espace non-commutatif". Lyon 1, 2005. http://tel.archives-ouvertes.fr/docs/00/06/71/64/PDF/these_matthieu_lefrancois.pdf.
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
Chau, Huu-Tai Pierre. "Symétrie et géométrie du problème à N-corps : application à la physique nucléaire". Caen, 2002. http://www.theses.fr/2002CAEN2029.
Pełny tekst źródłaMann, Etienne. "Cohomologie quantique orbifolde des espaces projectifs à poids". Phd thesis, Université Louis Pasteur - Strasbourg I, 2005. http://tel.archives-ouvertes.fr/tel-00011651.
Pełny tekst źródłaL'objectif de cette thèse est de généraliser ce résultat. Plus précisément, nous montrons, modulo une conjecture sur la valeur de certains invariants de Gromov-Witten orbifold, que la structure de Frobenius obtenue sur la cohomologie quantique orbifolde de l'espace projectif à poids est isomorphe à celle obtenue à partir d'un certain polynôme de Laurent.
Henry, Simon. "Des topos à la géométrie non commutative par l'étude des espaces de Hilbert internes". Paris 7, 2014. http://www.theses.fr/2014PA077255.
Pełny tekst źródłaThe goal of this thesis is to study some relations between non-commutative geometry and topos theory, as two generalisation of topology. The main tool we are using is the study of continuous bundles of Hilbert spaces over a topos which are defined as Hilbert spaces in the internai Iogic of the topos. By looking at the aigebras of bounded operators over such Hilbert spaces one can associate C*-aigebras to a topos. In chapter 1 we study this relation through the use of quantales, and in the case of at ic toposes. For such toposes the relation with operator aigebras can be described expl Ytely, and this provides an interesting toy-mode) for the case of more general toposes. In chapter 2 we focus on measure theoretic aspects. We define a notion of generalized measure ciass over a topos, and this notion appears to be closely related to the theory of W* aigebras. Lnspired by the results of chapter 1 we define a notion of invariant measure, which appears to be analogous to the notion of trace on a W*-algebra. The classification of such measures gives rise to a canonicat R+*-principal bundle on every integrable locally separate boolean topos, which is the analogue of the modular theory of W*-algebras. In chapter 3, we define and study a notion of localic Banach spaces. Our motivations are tha it allows to generalize the techniques used on toposes in this thesis to topological and localic groupoids, and to obtain an extension of the constructive Gelfand duality as conjectured by C. J. Mulvey and B. Banachewski. We also prove that over a topos satisfying a condition related to paracompactness, the notion of localic Banach space is equivalent to the usual notion of Banach space
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
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
Assemat, Elie. "Sur le rôle des singularités hamiltoniennes 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-00804765.
Pełny tekst źródłaBaratin, Aristide. "State sum structures in Feynman Diagrams". Lyon, École normale supérieure (sciences), 2009. http://www.theses.fr/2009ENSL0507.
Pełny tekst źródłaOne of the main challenges that `spin foam models' for quantum gravity have to face is to recover low energy physics in a suitable regime. The main goal in this work is to bring to light spin foam structures in the framework of standard quantum field theory. Feynman amplitudes are reformulated in terms as observables for a topological spin foam model. In dimension 3, the complete calculation of the 6j symbol for the group ISO(3) allows one to interpret the model as the discretized functional integral of a BF theory. In dimension 4, the analysis of the model reveals a 2-categorical structure related to the representations of the `Poincaré 2-group'. The in-depth mathematical study of this representation theory is the object of the mathematical part of this work. In light of the heuristic categorical approach sketched by Crane and Frenkel, this may open the way to the construction of new state sum invariants in four dimensions, of which the Feynman diagram spin foam model would be a concrete example
Aru, Juhan. "Géométrie du champ libre Gaussien en relation avec les processus SLE et la formule KPZ". Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL1007/document.
Pełny tekst źródłaIn this thesis we study the geometry of the Gaussian free field (GFF). After a gentle general introduction, we describe what we call the Hodge decomposition of the white noise – a way to represent the white noise vector field as a sum of a gradient and a rotation of independent GFFs. This decomposition gives rise to the Donsker invariance principle for the GFF.Next, we revisit from a slightly different angle the theory of so-called local sets of the GFF, introduced by Schramm and Sheffield. These random sets allow one to study the geometry of the GFF in a Markovian way. We also go a step further in describing the behaviour of the field near the boundary of possibly several local sets. The first chapter ends with a study of boundary oscillations of the GFF.The GFF is only a generalized function, yet it comes out that one can still make sense of it as a „random landscape“. In particular, Schramm and Sheffield gave meaning to the level lines of the GFF in terms of a coupling with SLE_4 process. In chapter 2 we study this coupling and describe the existent proofs and a non-proof of measurability of the SLE_4 process in this coupling. The rest of this chapter contains one of the most technical parts of the thesis – we obtain fine estimates on the winding of the SLE curves, conditioned to pass closely by a fixed point.This technical work is put in use in chapter 3, where we study the so called KPZ relation. In this context, the KPZ formula relates fractal dimensions of sets under the Euclidean geometry and under the „quantum geometry“ given by the exponential of the GFF. So far the KPZ formula was derived for planar sets independent of the quantum geometry. Here, we determine the KPZ formulas for sets that are naturally coupled with the quantum geometry – for the flow and level lines of the GFF. The family of KPZ formulas obtained resemble but still differ from the KPZ formula for independent sets
Ben, Aicha Ibtissem. "Etude mathématique de problèmes inverses non autonomes de types hyperbolique et quantique". Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4114/document.
Pełny tekst źródłaThis thesis is devoted to the study of inverse problems associated to hyperbolic and Schrödinger equations. The first part of the thesis is devoted to the study of inverse problemsfor the wave equation. The aim is to examine the stability andthe uniqueness issues in the identification of certain coefficients appearing in the wave equation from different types of observation. The second part of this thesis deals with the problem of the identification of a magnetic field and an electric potential appearing in the Schrödinger equation. We prove that these coefficients can be stably determined throughout the domain, using Neumann data. The derivation of these results is based on the construction of a set of geometric optics solutions adapted to the system studied. There is an alternative method for the analysis of this type of inverse problem, which is due to Bukhgeim-Klibanov, and which uses a Carleman estimate. We show that it is possible to stably and simultaneously recover the spatial part of the electrical and magnetic potentialsappearing in the magnetic Schrödinger equation, from a finite number of measurements
Wieland, Wolfgang Martin. "The Chiral Structure of Loop Quantum Gravity". Phd thesis, Aix-Marseille Université, 2013. http://tel.archives-ouvertes.fr/tel-00952498.
Pełny tekst źródłaWang, Zhituo. "La renormalisation constructive pour la théorie quantique des champs non commutative". Phd thesis, Université Paris Sud - Paris XI, 2011. http://tel.archives-ouvertes.fr/tel-00657010.
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