Aspects of classical and quantum motion on a flux cone

Motion of a nonrelativistic particle on a cone with a magnetic flux running through the cone axis (a flux cone) is studied. It is expressed as the motion of a particle moving on the Euclidean plane under the action of a velocity-dependent force. The probability fluid (quantum flow) associated with a particular stationary state is studied close to the singularity, demonstrating nontrivial Aharonov-Bohm effects. For example, it is shown that, near the singularity, quantum flow departs from classical flow. In the context of the hydrodynamical approach to quantum mechanics, quantum potential due to the conical singularity is determined, and the way it affects quantum flow is analyzed. It is shown that the winding number of classical orbits plays a role in the description of the quantum Bow. The connectivity of the configuration space is also discussed.

Classical and quantum N = 1 super W∞-algebras

We construct higher-spin N = 1 superalgebras as extensions of the super-Virasoro algebra containing generators for all spins s ≥ 3/2. We find two distinct classical (Poisson) algebras on the phase superspace. Our results indicate that only one of them can be consistently quantized.

The relation between geometry and matter in classical and quantum gravity and cosmology

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

Inverse problems in classical and quantum physics

The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A promising result is that one can qualitatively reconstruct the conductivity inside the cross-section of a human chest. Even though the human volunteer is neither two-dimensional nor circular, such reconstructions can be useful in medical applications: monitoring for lung problems such as accumulating fluid or a collapsed lung and noninvasive monitoring of heart function and blood flow.

Classical and quantum aspects of black hole dynamics

Il contenuto fisico della Relatività Generale è espresso dal Principio di Equivalenza, che sancisce l'equivalenza di geometria e gravitazione. La teoria predice l'esistenza dei buchi neri, i più semplici oggetti macroscopici esistenti in natura: essi sono infatti descritti da pochi parametri, le cui variazioni obbediscono a leggi analoghe a quelle della termodinamica. La termodinamica dei buchi neri è posta su basi solide dalla meccanica quantistica, mediante il fenomeno noto come radiazione di Hawking. Questi risultati gettano una luce su una possibile teoria quantistica della gravitazione, ma ad oggi una simile teoria è ancora lontana. In questa tesi ci proponiamo di studiare i buchi neri nei loro aspetti sia classici che quantistici. I primi due capitoli sono dedicati all'esposizione dei principali risultati raggiunti in ambito teorico: in particolare ci soffermeremo sui singularity theorems, le leggi della meccanica dei buchi neri e la radiazione di Hawking. Il terzo capitolo, che estende la discussione sulle singolarità, espone la teoria dei buchi neri non singolari, pensati come un modello effettivo di rimozione delle singolarità. Infine il quarto capitolo esplora le ulteriori conseguenze della meccanica quantistica sulla dinamica dei buchi neri, mediante l'uso della nozione di entropia di entanglement.

Classical and quantum dynamics of a model for atomic-molecular Bose-Einstein condensates

We study a model for a two-mode atomic-molecular Bose-Einstein condensate. Starting with a classical analysis we determine the phase space fixed points of the system. It is found that bifurcations of the fixed points naturally separate the coupling parameter space into four regions. The different regions give rise to qualitatively different dynamics. We then show that this classification holds true for the quantum dynamics.

Classical and quantum approaches to the interaction of light and matter at the nanoscale

168 p.

Non-Markovianity and Quantum Correlations in Qubit-Systems

In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. In the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. In the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. The dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.

Gravitation: global formulation and quantum effects

A non-integrable phase-factor global approach to gravitation is developed by using the similarity of teleparallel gravity to electromagnetism. The phase shifts of both the COW and the gravitational Aharonov-Bohm effects are obtained. It is then shown, by considering a simple slit experiment, that in the classical limit the global approach yields the same result as the gravitational Lorentz force equation of teleparallel gravity. It represents, therefore, the quantum mechanical version of the classical description provided by the gravitational Lorentz force equation. As teleparallel gravity can be formulated independently of the equivalence principle, it will consequently require no generalization of this principle at the quantum level.

From Classical to Quantum Secret Sharing

Dans ce mémoire, nous nous pencherons tout particulièrement sur une primitive cryptographique connue sous le nom de partage de secret. Nous explorerons autant le domaine classique que le domaine quantique de ces primitives, couronnant notre étude par la présentation d’un nouveau protocole de partage de secret quantique nécessitant un nombre minimal de parts quantiques c.-à-d. une seule part quantique par participant. L’ouverture de notre étude se fera par la présentation dans le chapitre préliminaire d’un survol des notions mathématiques sous-jacentes à la théorie de l’information quantique ayant pour but primaire d’établir la notation utilisée dans ce manuscrit, ainsi que la présentation d’un précis des propriétés mathématique de l’état de Greenberger-Horne-Zeilinger (GHZ) fréquemment utilisé dans les domaines quantiques de la cryptographie et des jeux de la communication. Mais, comme nous l’avons mentionné plus haut, c’est le domaine cryptographique qui restera le point focal de cette étude. Dans le second chapitre, nous nous intéresserons à la théorie des codes correcteurs d’erreurs classiques et quantiques qui seront à leur tour d’extrême importances lors de l’introduction de la théorie quantique du partage de secret dans le chapitre suivant. Dans la première partie du troisième chapitre, nous nous concentrerons sur le domaine classique du partage de secret en présentant un cadre théorique général portant sur la construction de ces primitives illustrant tout au long les concepts introduits par des exemples présentés pour leurs intérêts autant historiques que pédagogiques. Ceci préparera le chemin pour notre exposé sur la théorie quantique du partage de secret qui sera le focus de la seconde partie de ce même chapitre. Nous présenterons alors les théorèmes et définitions les plus généraux connus à date portant sur la construction de ces primitives en portant un intérêt particulier au partage quantique à seuil. Nous montrerons le lien étroit entre la théorie quantique des codes correcteurs d’erreurs et celle du partage de secret. Ce lien est si étroit que l’on considère les codes correcteurs d’erreurs quantiques étaient de plus proches analogues aux partages de secrets quantiques que ne leur étaient les codes de partage de secrets classiques. Finalement, nous présenterons un de nos trois résultats parus dans A. Broadbent, P.-R. Chouha, A. Tapp (2009); un protocole sécuritaire et minimal de partage de secret quantique a seuil (les deux autres résultats dont nous traiterons pas ici portent sur la complexité de la communication et sur la simulation classique de l’état de GHZ).

Gravitational deflection of massive particles in classical and semiclassical general relativity

We calculate the gravitational deflection of massive particles moving with relativistic velocity in the solar system to second post-Newtonian order. For a particle passing close to the Sun with impact parameter b, the deflection in classical general relativity is Phi(C)[GRAPHICS]where v(0) is the particle speed at infinity and M is the Sun's mass. We compute afterwards the gravitational deflection of a spinless neutral particle of mass m in the same static gravitational field as above, treated now as an external field. For a scalar boson with energy E, the deflection in semiclassical general relativity (SGR) is Phisc[GRAPHICS]This result shows that the propagation of the =2E spinless massive boson produces inexorably dispersive effects. It also shows that the semiclassical prediction is always greater than the geometrical one, no matter what the boson mass is. In addition, it is found that SGR predicts a deflection angle of similar to2.6 arcsec for a nonrelativistic spinless massive boson passing at the Sun's limb.

Gravitational and quantum bounds on the photon mass

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)