• Refine Query
  • Source
  • Publication year
  • to
  • Language
  • 13
  • 4
  • 3
  • 2
  • 1
  • 1
  • 1
  • Tagged with
  • 28
  • 19
  • 19
  • 11
  • 10
  • 9
  • 7
  • 6
  • 6
  • 5
  • 5
  • 4
  • 4
  • 4
  • 3
  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Stochastic thermodynamics for open quantum systems in the reapeated interaction scheme

Lledo Veloso, Cristóbal January 2017 (has links)
Magíster en Ciencias, Mención Física / Usamos la teoría de termodinámica estocástica para estudiar sistemas cuánticos cuya dinámica es descrita por mapas completamente positivos que preservan la traza (CPTP en inglés) debido a su interacción con un baño térmico. Estudiamos una clase más amplia de mapas con equilibrio, entre los cuales los mapas termales son solo un caso especial. En general, para mapas CPTP las cantidades termodinámicas tales como la producción de entropía y el trabajo realizado sobre el sistema dependen del estado combinado del sistema más baño. Mostramos que para mapas con equilibrio estas cantidades pueden ser escritas en términos de propiedades del sistema únicamente. Las relaciones que obtenemos son válidas para una intensidad de acoplamiento arbitraria entre el sistema y el baño termal. Estudiamos las fluctuaciones de las cantidades termodinámicas en el esquema de medición de dos puntos. Derivamos teoremas de fluctuación detallados para la producción de entropía y el trabajo y obtemos algunas simplificaciones para el caso de los mapas con equilibrio. Ilustramos nuestros resultados considerando un espín en un ciclo termodinámico y una cadena de espines 1/2 acopladas a un baño por uno de sus bordes. Conectamos además la condición de balance detallado cuántico para ecuaciones maestras de Lindblad con la propiedad de equilibrio de los mapas CPTP que, al iterarlos y en un límite particular, generan la ecuación maestra. Mostramos cómo obtener una concatenación de mapas que genera una ecuación de Lindblad forzada por los bordes dada apriori, como una forma de construir una termodinámica consistente para la dinámica de Lindblad. / Este trabajo ha sido parcialmente financiado por Conicyt a través de becas Magíster Nacional 2016, contrato N° 22161809
2

La fonction d'onde du photon en principe et en pratique / The Photon Wave Function in Principle and in Practice

Debierre, Vincent 25 September 2015 (has links)
Pendant ces trois ans, nous nous sommes intéressés à quelques sujets choisis en optique et en électrodynamique quantiques. Le fil rouge de nos interrogations est la fonction d’onde du photon. Les expériences d’optique et d’électrodynamique quantique peuvent-elles être décrites de manière simple, dans l’espace des positions, à l’aide d’une fonction d’onde décrivant le ou les photon(s) impliqués dans l’expérience ? Ce n’est pas entièrement évident :la description usuelle des photons se fait dans l’espace réciproque des vecteurs d’onde. Mais ces expériences gagnent à être décrites par la mécanique ondulatoire en représentation position, comme cela est fait dans les manuels de mécanique quantique pour des situations impliquant des particules massives. De surcroît, une expérience récente[1] a conduit à l’observation de trajectoires de photons uniques à travers un interféromètre à deux fentes d’Young.Pour essayer de décrire formellement ces trajectoires, il est naturel de formuler une mécanique ondulatoire pour les photons. Nous avons donc examiné en détail la construction formelle de la fonction d’onde du photon, un objet qui est resté peu étudié jusqu’aux années 1990. Nous avons également étudié les propriétés de la fonction d’onde du photon en présence de sources, et considéré pour ce faire divers systèmes quantiques ouverts (en interaction). Nous avons vu qu’il existe, en principe, une infinité de possibilités pour le choix de la fonction d’onde du photon.Nous avons mis en évidence un certain nombre de critères sur la base desquels il apparaît que seuls trois choix parmi tous ceux possibles sont intéressants, l’un d’entre eux ramenant à un objet introduit par Glauber [2] pour étudier la détection de la lumière et les corrélations du champ électromagnétique. Nous avons également vu qu’en l’absence de sources l’équation quantique de propagation des photons est formellement identique aux équations de Maxwell.À bas nombre de photons, le formalisme de la fonction d’onde peut se révéler très pratique. Nous avons adapté l’approche aux systèmes en interaction, en nous intéressant dans un premier temps à l’électrodynamique quantique1en cavité [3], en particulier aux expériences réalisées par le groupe de Serge Haroche [4]. Nous avons proposé un modèle simple pour la description des photons dans les cavités d’électrodynamique. À l’aide de ce modèle, et de la fonction d’onde du photon, nous avons étudié la propagation des photons s’échappant de la cavité. Nous avons également construit l’équation maîtresse de Lindblad sans introduire de sauts quantiques non unitaires (voir également [5]). Nous nous sommes enfin intéressés à la question de l’évolution spatiotemporelle d’un photon émis lors d’une désexcitation d’un électron atomique. Après avoir étudié soigneusement la dynamique de la désexcitation de l’électron, notamment aux temps très courts [6, 7], nous nous sommes attachés à décrire, aussi rigoureusement que possible, le champ électromagnétique émis. Celui-ci, de manière surprenante, n’évolue pas causalement. Si cela n’est pas entièrement inattendu au vu du théorème de Hegerfeldt, qui stipule [8] que la causalité est exclue pour les systèmes décrits par un Hamiltonien dont le spectre est borné inférieurement, nous avons identifié [9] deux autres sources de non-causalité, l’une, prédite qualitativement par Shirokov [10], et l’autre, entièrement nouvelle à notre connaissance, et dont la compréhension reste à affiner. / During these three years we focused on several topics in quantum otpics and quantum electrodynamics. A central theme in our investigations is that of the photon wave function. Can quantum optics and quantum electrodynamics experiments be described simply, in position space, with the help of a wave function describing the photon(s) featured in the experiment ? The answer to that question is not quite obvious: the usual description of photons takes place in the reciprocal space of wave vectors. But these experiments call for a wave mechanical description in the position representation, as is done in quantum mechanics textbooks in situations featuring massive particles. Moreover, in a recent experiment [1], single photon trajectories through a Young two-slit setup have been observed. In order to try and describe these trajectories formally, it is natural to build a wave mechanical formalism for photons. We therefore studied in detail the formal construction of the photon wave function, an object which was little studied until the 1990s. We also studied the properties of the photon wave function in the presence of sources.To do that, we considered several open (interacting) quantum systems. We saw that there exists in principle an infinite number of possibilities when defining the photon wave function. We emphasised several criteria on the basis of which it appears that only three choices for the wave function are interesting. One of them coincides with an object introduced and used by Glauber [2] to study light detection andthe correlations of the electromagnetic field in the quantum regime. We also saw that, in the absence of sources, the propagation equation for a single photon is formally equivalent to Maxwell’s equations. At low photon numbers, the wave function formalism can be very useful. We adapted it to interacting systems,first, to cavity quantum electrodynamics (QED) [3], in particular to the experiments carried out by Serge Haroche’s group [4]. We proposed a simple model to describe photons in QED cavities. With this model, and with the helpof the photon wave function, we studied the propagation of photons escaping a cavity. We also constructed the Lindblad master equation without introducing nonunitary quantum jumps (also see [5]). We finally investigated the spacetime evolution of a photon which is emitted during the decay of an atomic electron. After having carefully studied the dynamics of the electronic decay, especially at very short times [6, 7], we set out to describe the emitted electromagnetic field as rigorously as possible. This emitted field, surprisingly, does not evolve causally. Though this is not entirely unexpected in view of Hegerfeldt’s theorem, which states [8] that causality is impossible for quantum systems which are described by a Hamiltonian with a spectrum which is bounded by below, we identified [9] two other sources of non causality. One of them was predicted qualitatively by Shirokov [10], while the other one, which is completely new as far as we can tell, is still to be better understood
3

Exploring Quantum Chaos in a Spin 1/2 Atom Driven by a 3D Chaotic Magnetic Field

Goettemoeller, Jared 04 August 2017 (has links)
No description available.
4

Evolution of a 1D bipartite fermionic chain under in?uence of a phenomenological dephasing

Ribeiro, Wellington Luiz January 2018 (has links)
Orientador: Prof. Dr. Gabriel Teixeira Landi / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, Santo André, 2018. / Em sistemas microscópicos, grandezas como calor e trabalho devem ser tratadas como variáveis aleatórias. Neste trabalho foram estudados os fluxos de calor e de partículas entre dois sistemas unidimensionais fermiônicos A eB, inicialmente preparados separadamente em equilíbrio térmico com reservatórios de calor e partículas preparados a diferentes temperaturas e diferentes potenciais químicos. Calculando a evolução da matriz densidade, foram analisadas as implicações da presença de um ruído de dephasing no sistema, tais como a termalização, a produção de entropia e a evolução da informação mútua como uma forma de analisar a correlação entre os sistemas. Além disso, foi estudado também uma forma do teorema de flutuação do calor no caso onde há fluxo de partículas. / In microscopic systems, heat and work must be treated as random variables. In this work I studied the fluxes of heat and particles between two unidimentional fermionic systems A and B, initially prepared in thermal equilibrium with a reservoir of particles and heat, kept at diferent temperatures and chemical potentials. Computing the evolution of the density matrix, the implications of the presence of a dephasing noise in the system were analyzed, such as thermalization, entropy production and the evolution of mutual information as a way to analyze the correlation between the systems. Moreover, a shape for fluctuation theorems of the heat in the case where there is also a ?ux of particles and its validity was also studied.
5

On the controllability of the quantum dynamics of closed and open systems / Sur la contrôlabilité de la dynamique quantique des systèmes fermés et ouverts

Pinna, Lorenzo 26 January 2018 (has links)
On etudie la contrôlabilité des systèmes quantiques dans deux contextes différents: le cadre standard fermé, dans lequel un système quantique est considéré comme isolé et le problème de contrôle est formulé sur l'équation de Schrödinger; le cadre ouvert qui décrit un système quantique en interaction avec un plus grand, dont seuls les paramètres qualitatifs sont connus, au moyen de l'équation de Lindblad sur les états.Dans le contexte des systèmes fermés on se focalise sur la classe intéressante des systèmes spin-boson, qui décrivent l'interaction entre un système quantique à deux niveaux et un nombre fini de modes distingués d'un champ bosonique. On considère deux exemples prototypiques, le modèle de Rabi et le modèle de Jaynes-Cummings qui sont encore très populaires dans plusieurs domaines de la physique quantique. Notamment, dans le contexte de la Cavity Quantum Electro Dynamics (C-QED), ils fournissent une description précise de la dynamique d'un atome à deux niveaux dans une cavité micro-onde en résonance, comme dans les expériences récentes de S. Haroche. Nous étudions les propriétés de contrôlabilité de ces modèles avec deux types différents d'opérateurs de contrôle agissant sur la partie bosonique, correspondant respectivement – dans l'application à la C-QED – à un champ électrique et magnétique externe. On passe en revue quelques résultats récents et prouvons la contrôlabilité approximative du modèle de Jaynes-Cummings avec ces contrôles. Ce résultat est basé sur une analyse spectrale exploitant les non-résonances du spectre. En ce qui concerne la relation entre l'Hamiltonien de Rabi et Jaynes-Cummings nous traitons dans un cadre rigoureux l'approximation appelée d'onde tournante. On formule le problème comme une limite adiabatique dans lequel la fréquence de detuning et le paramètre de force d'interaction tombent à zero, ce cas est connu sous le nom de régime de weak-coupling. On prouve que, sous certaines hypothèses sur le rapport entre le detuning et le couplage, la dynamique de Jaynes-Cumming et Rabi montrent le même comportement, plus précisément les opérateurs d'évolution qu'ils génèrent sont proches à la norme.Dans le cadre des systèmes quantiques ouverts nous étudions la contrôlabilité de l'équation de Lindblad. Nous considérons un contrôle agissant adiabatiquement sur la partie interne du système, que nous voyons comme un degré de liberté qui peut être utilisé pour contraster l'action de l'environnement. L'action adiabatique du contrôle est choisie pour produire une transition robuste. On prouve, dans le cas prototype d'un système à deux niveaux, que le système approche un ensemble de points d'équilibre déterminés par l'environnement, plus précisément les paramètres qui spécifient l'opérateur de Lindblad. Sur cet ensemble, le système peut être piloté adiabatiquement en choisissant un contrôle approprié. L'analyse est fondée sur l'application de méthodes de perturbation géométrique singulière. / We 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.
6

Dynamics of Nuclear Clusters in Neutron Stars / Dynamik hos nukleära kluster i neutronstjärnor

Cheragwandi, Twana January 2024 (has links)
The inner crust of a neutron star is explored, using nuclear models andimplementing them in an open quantum system formalism. The purposeof the investigation is to extract valuable dynamics of the predictednuclear clusters that may exist in this region. We begin by setting up thenuclear models to extract the total energy per particle per system in orderto see if the results are corroborated with the works of others. Thereafter,the single-particle energies of the nuclear clusters are extracted. Theseenergies are then used in the Lindblad formalism to work out the timedependenceof the density matrix, which will allow us to extract thetime-dependence of the average energy of the system in interaction withan environment. / Den inre skorpan hos en neutronstjärna utforskas genom att användakärnmodeller och implementera dem i en öppen kvantumsystemformalism.Syftet med undersökningen är att extrahera värdefulladynamiska egenskaper hos de förutsagda kärnkluster som kan existerai detta område. Vi börjar med att etablera kärnmodeller för att extrahera den totala energin per partikel per system för att se omresultaten överensstämmer med andras arbeten. Därefter extraherade enskilda partikelenergierna hos kärnklusterna. Dessa energieranvänds sedan i Lindblad-formalismen för att beräkna tidsberoendetav densitetsmatrisen, vilket kommer att tillåta oss att extraheratidsberoendet av systemets genomsnittliga energi i interaktion med en miljö.
7

Descrição de medidas em sistemas de 2 níveis pela equação de Lindblad com inclusão de ambiente / Analysis of the environmental influence on the measurement process of a 2-level system using the Lindblad equation

Brasil, Carlos Alexandre 23 February 2012 (has links)
O objetivo deste trabalho é explorar um modelo para medidas quânticas de duração finita baseado na equação de Lindblad, com a análise de um sistema de 2 níveis acoplado a um reservatório térmico que ocasiona decoerência. A interação entre o sistema e o dispositivo de medida é markoviana, justificando o uso da equação de Lindblad para obter a dinâmica do processo de medida. Para analisar a influência do ambiente/reservatório térmico não-markoviano, cuja definição não inclui o aparato de medida, foi utilizada a abordagem de Redfield para a interação entre o sistema e o ambiente. Na teoria híbrida aqui exposta, para efetuar o traço parcial dos graus de liberdade do ambiente foi desenvolvido um método analítico baseado na álgebra de super-operadores e no uso dos super-operadores de Nakajima-Zwanzig. Foi verificado que medidas de duração finita sobre o sistema aberto de 2 níveis podem proteger o estado inicial dos efeitos do ambiente, desde que o observável medido não comute com a interação. Quando o observável medido comuta com a interação sistema-ambiente, a medida de duração finita acelera a decoerência induzida pelo ambiente. A validade das previsões analíticas foi testada comparando os resultados com uma abordagem numérica exata. Quando o acoplamento entre o sistema e o aparato de medida excede a faixa de validade da aproximação analítica, o estado inicial ainda é protegido pela medida de duração finita, como indicam os cálculos numéricos exatos. / The aim of this work is to explore a model for finite-time measurement based on the Lindblad equation, with analysis of a system consisting of a 2-level system coupled to a thermal reservoir. We assume a Markovian measuring device and, therefore, use a Lindbladian description for the measurement dynamics. For studying the case of noise produced by a non-Markovian environment, whose definition does not include the measuring apparatus, we use the Redfield approach to the interaction between system and environment. In the present hybrid theory, to trace out the environmental degrees of freedom, we introduce an analytic method based on superoperator algebra and Nakajima-Zwanzig superoperators. We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. We have tested the validity of the analytical predictions against an exact numerical approach. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.
8

Fenômenos de transporte em sistemas fora do equilíbrio / Transport Phenomena in Out-of-Equilibrium Systems

Santos, Pedro Henrique Guimarães dos 04 July 2017 (has links)
Fenômenos de transporte constituem um dos grandes desafios teóricos da mecânica estatística fora do equilíbrio, uma vez que a compreensão dos mecanismos microscópicos que regem tais fenômenos não está completamente estabelecida. Conduzidos, portanto, pela motivação de melhor compreender esses mecanismos, propomos nesta tese o estudo dos fenômenos de transporte através de dois modelos microscópicos em dois contextos distintos: clássico e quântico. No contexto clássico, consideramos como modelo uma cadeia de osciladores harmônicos acoplados, sujeita a um potencial local (pinning) anarmônico quártico (conhecido como modelo phi4). A cadeia está em contato, através de suas extremidades, com dois reservatórios térmicos mantidos a temperaturas distintas, e sua dinâmica é dada por um sistema de equações de Langevin. Além disso, consideramos a inclusão de um ruído conservativo que inverte aleatoriamente o sentido da velocidade de cada partícula. Nesse sistema, estudamos dois fenômenos de transporte associados à condução de calor: a Lei de Fourier e a retificação térmica. Os resultados foram obtidos numericamente através da simulação do sistema usando-se métodos de dinâmica estocástica. A partir desses resultados pudemos concluir que, tanto a validade da Lei de Fourier, quanto a presença de uma retificação finita no limite termodinâmico, estão associadas à presença do ruído conservativo na dinâmica do sistema. No contexto quântico, utilizamos como modelo de trabalho uma cadeia de spins do tipo XX posta em contato, através de suas extremidades, com dois reservatórios mantidos a diferentes temperaturas e potenciais químicos. A interação com os reservatórios foi feita através de dissipadores de Lindblad presentes na equação mestra quântica que fornece a dinâmica do sistema. Esses dissipadores são acoplados aos modos normais do hamiltoniano do modelo de forma que, no equilíbrio, o sistema termaliza corretamente para o estado de Gibbs. Além de resultados numéricos, obtivemos através de um método perturbativo, expressões analíticas para os fluxos de energia e de partículas ao longo da cadeia, verificando que ambos possuem a estrutura da fórmula de Landauer. No regime em que o acoplamento com os reservatórios é fraco, verificamos ainda que as relações de reciprocidade de Onsager entre esses fluxos são satisfeitas. / Transport phenomena are one of the great theoretical challenges of out-of-equilibrium statistical mechanics since the understanding of the microscopic mechanisms governing such phenomena is not yet fully established. To better understand these mechanisms, we propose in this thesis the study of transport phenomena through two microscopic models in two distinct contexts: classical and quantum ones. In the classical context, we considered as a working model a chain of coupled harmonic oscillators, subject to a quartic anharmonic pinning (known as the phi4 model). The chain is in contact, through its ends, with two thermal reservoirs kept at different temperatures, and its dynamics is given by a system of Langevin equations. In addition, we considered the inclusion of a conservative noise that randomly reverses the direction of the velocity of each particle. In this system, we studied two transport phenomena associated with heat conduction: the Fourier Law and the thermal rectification. The results were obtained numerically by simulating the system using stochastic dynamics methods. From these results we concluded that both the validity of the Fourier Law and the presence of a finite rectification in the thermodynamic limit are associated with the presence of the conservative noise in the system dynamics. In the quantum context, we used as a working model the XX spin chain that was put in contact, through its ends, with two reservoirs kept at different temperatures and chemical potentials. The interaction with the reservoirs was modeled through Lindblad dissipators included in the quantum master equation that describes the system dynamics. These dissipators are coupled to the normal modes of the model Hamiltonian so that, in equilibrium, the system thermalizes correctly to the Gibbs state. In addition to numerical results, we obtained through a perturbative method, analytical expressions for the energy and particle fluxes along the chain, verifying that both have the structure of the Landauer formula. In the regime where the coupling with the reservoirs is weak, we also verified that the Onsager reciprocal relations between these fluxes are satisfied.
9

Fenômenos de transporte em sistemas fora do equilíbrio / Transport Phenomena in Out-of-Equilibrium Systems

Pedro Henrique Guimarães dos Santos 04 July 2017 (has links)
Fenômenos de transporte constituem um dos grandes desafios teóricos da mecânica estatística fora do equilíbrio, uma vez que a compreensão dos mecanismos microscópicos que regem tais fenômenos não está completamente estabelecida. Conduzidos, portanto, pela motivação de melhor compreender esses mecanismos, propomos nesta tese o estudo dos fenômenos de transporte através de dois modelos microscópicos em dois contextos distintos: clássico e quântico. No contexto clássico, consideramos como modelo uma cadeia de osciladores harmônicos acoplados, sujeita a um potencial local (pinning) anarmônico quártico (conhecido como modelo phi4). A cadeia está em contato, através de suas extremidades, com dois reservatórios térmicos mantidos a temperaturas distintas, e sua dinâmica é dada por um sistema de equações de Langevin. Além disso, consideramos a inclusão de um ruído conservativo que inverte aleatoriamente o sentido da velocidade de cada partícula. Nesse sistema, estudamos dois fenômenos de transporte associados à condução de calor: a Lei de Fourier e a retificação térmica. Os resultados foram obtidos numericamente através da simulação do sistema usando-se métodos de dinâmica estocástica. A partir desses resultados pudemos concluir que, tanto a validade da Lei de Fourier, quanto a presença de uma retificação finita no limite termodinâmico, estão associadas à presença do ruído conservativo na dinâmica do sistema. No contexto quântico, utilizamos como modelo de trabalho uma cadeia de spins do tipo XX posta em contato, através de suas extremidades, com dois reservatórios mantidos a diferentes temperaturas e potenciais químicos. A interação com os reservatórios foi feita através de dissipadores de Lindblad presentes na equação mestra quântica que fornece a dinâmica do sistema. Esses dissipadores são acoplados aos modos normais do hamiltoniano do modelo de forma que, no equilíbrio, o sistema termaliza corretamente para o estado de Gibbs. Além de resultados numéricos, obtivemos através de um método perturbativo, expressões analíticas para os fluxos de energia e de partículas ao longo da cadeia, verificando que ambos possuem a estrutura da fórmula de Landauer. No regime em que o acoplamento com os reservatórios é fraco, verificamos ainda que as relações de reciprocidade de Onsager entre esses fluxos são satisfeitas. / Transport phenomena are one of the great theoretical challenges of out-of-equilibrium statistical mechanics since the understanding of the microscopic mechanisms governing such phenomena is not yet fully established. To better understand these mechanisms, we propose in this thesis the study of transport phenomena through two microscopic models in two distinct contexts: classical and quantum ones. In the classical context, we considered as a working model a chain of coupled harmonic oscillators, subject to a quartic anharmonic pinning (known as the phi4 model). The chain is in contact, through its ends, with two thermal reservoirs kept at different temperatures, and its dynamics is given by a system of Langevin equations. In addition, we considered the inclusion of a conservative noise that randomly reverses the direction of the velocity of each particle. In this system, we studied two transport phenomena associated with heat conduction: the Fourier Law and the thermal rectification. The results were obtained numerically by simulating the system using stochastic dynamics methods. From these results we concluded that both the validity of the Fourier Law and the presence of a finite rectification in the thermodynamic limit are associated with the presence of the conservative noise in the system dynamics. In the quantum context, we used as a working model the XX spin chain that was put in contact, through its ends, with two reservoirs kept at different temperatures and chemical potentials. The interaction with the reservoirs was modeled through Lindblad dissipators included in the quantum master equation that describes the system dynamics. These dissipators are coupled to the normal modes of the model Hamiltonian so that, in equilibrium, the system thermalizes correctly to the Gibbs state. In addition to numerical results, we obtained through a perturbative method, analytical expressions for the energy and particle fluxes along the chain, verifying that both have the structure of the Landauer formula. In the regime where the coupling with the reservoirs is weak, we also verified that the Onsager reciprocal relations between these fluxes are satisfied.
10

Descrição de medidas em sistemas de 2 níveis pela equação de Lindblad com inclusão de ambiente / Analysis of the environmental influence on the measurement process of a 2-level system using the Lindblad equation

Carlos Alexandre Brasil 23 February 2012 (has links)
O objetivo deste trabalho é explorar um modelo para medidas quânticas de duração finita baseado na equação de Lindblad, com a análise de um sistema de 2 níveis acoplado a um reservatório térmico que ocasiona decoerência. A interação entre o sistema e o dispositivo de medida é markoviana, justificando o uso da equação de Lindblad para obter a dinâmica do processo de medida. Para analisar a influência do ambiente/reservatório térmico não-markoviano, cuja definição não inclui o aparato de medida, foi utilizada a abordagem de Redfield para a interação entre o sistema e o ambiente. Na teoria híbrida aqui exposta, para efetuar o traço parcial dos graus de liberdade do ambiente foi desenvolvido um método analítico baseado na álgebra de super-operadores e no uso dos super-operadores de Nakajima-Zwanzig. Foi verificado que medidas de duração finita sobre o sistema aberto de 2 níveis podem proteger o estado inicial dos efeitos do ambiente, desde que o observável medido não comute com a interação. Quando o observável medido comuta com a interação sistema-ambiente, a medida de duração finita acelera a decoerência induzida pelo ambiente. A validade das previsões analíticas foi testada comparando os resultados com uma abordagem numérica exata. Quando o acoplamento entre o sistema e o aparato de medida excede a faixa de validade da aproximação analítica, o estado inicial ainda é protegido pela medida de duração finita, como indicam os cálculos numéricos exatos. / The aim of this work is to explore a model for finite-time measurement based on the Lindblad equation, with analysis of a system consisting of a 2-level system coupled to a thermal reservoir. We assume a Markovian measuring device and, therefore, use a Lindbladian description for the measurement dynamics. For studying the case of noise produced by a non-Markovian environment, whose definition does not include the measuring apparatus, we use the Redfield approach to the interaction between system and environment. In the present hybrid theory, to trace out the environmental degrees of freedom, we introduce an analytic method based on superoperator algebra and Nakajima-Zwanzig superoperators. We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. We have tested the validity of the analytical predictions against an exact numerical approach. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

Page generated in 0.1069 seconds