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Non-Markovian Dissipative Quantum Mechanics with Stochastic TrajectoriesKoch, Werner 20 January 2011 (has links) (PDF)
All fields of physics - be it nuclear, atomic and molecular, solid state, or optical - offer examples of systems which are strongly influenced by the environment of the actual system under investigation. The scope of what is called "the environment" may vary, i.e., how far from the system of interest an interaction between the two does persist. Typically, however, it is much larger than the open system itself. Hence, a fully quantum mechanical treatment of the combined system without approximations and without limitations of the type of system is currently out of reach.
With the single assumption of the environment to consist of an internally thermalized set of infinitely many harmonic oscillators, the seminal work of Stockburger and Grabert [Chem. Phys., 268:249-256, 2001] introduced an open system description that captures the environmental influence by means of a stochastic driving of the reduced system. The resulting stochastic Liouville-von Neumann equation describes the full non-Markovian dynamics without explicit memory but instead accounts for it implicitly through the correlations of the complex-valued noise forces.
The present thesis provides a first application of the Stockburger-Grabert stochastic Liouville-von Neumann equation to the computation of the dynamics of anharmonic, continuous open systems. In particular, it is demonstrated that trajectory based propagators allow for the construction of a numerically stable propagation scheme. With this approach it becomes possible to achieve the tremendous increase of the noise sample count necessary to stochastically converge the results when investigating such systems with continuous variables. After a test against available analytic results for the dissipative harmonic oscillator, the approach is subsequently applied to the analysis of two different realistic, physical systems.
As a first example, the dynamics of a dissipative molecular oscillator is investigated. Long time propagation - until thermalization is reached - is shown to be possible with the presented approach. The properties of the thermalized density are determined and they are ascertained to be independent of the system's initial state. Furthermore, the dependence on the bath's temperature and coupling strength is analyzed and it is demonstrated how a change of the bath parameters can be used to tune the system from the dissociative to the bound regime.
A second investigation is conducted for a dissipative tunneling scenario in which a wave packet impinges on a barrier. The dependence of the transmission probability on the initial state's kinetic energy as well as the bath's temperature and coupling strength is computed.
For both systems, a comparison with the high-temperature Markovian quantum Brownian limit is performed. The importance of a full non-Markovian treatment is demonstrated as deviations are shown to exist between the two descriptions both in the low temperature cases where they are expected and in some of the high temperature cases where their appearance might not be anticipated as easily.
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Designing and Probing Open Quantum Systems: Quantum Annealing, Excitonic Energy Transfer, and Nonlinear Fluorescence SpectroscopyPerdomo, Alejandro 27 July 2012 (has links)
The 20th century saw the first revolution of quantum mechanics, setting the rules for our understanding of light, matter, and their interaction. The 21st century is focused on using these quantum mechanical laws to develop technologies which allows us to solve challenging practical problems. One of the directions is the use quantum devices which promise to surpass the best computers and best known classical algorithms for solving certain tasks. Crucial to the design of realistic devices and technologies is to account for the open nature of quantum systems and to cope with their interactions with the environment. In the first part of this dissertation, we show how to tackle classical optimization problems of interest in the physical sciences within one of these quantum computing paradigms, known as quantum annealing (QA). We present the largest implementation of QA on a biophysical problem (six different experiments with up to 81 superconducting quantum bits). Although the cases presented here can be solved on a classical computer, we present the first implementation of lattice protein folding on a quantum device under the Miyazawa-Jernigan model. This is the first step towards studying optimization problems in biophysics and statistical mechanics using quantum devices. In the second part of this dissertation, we focus on the problem of excitonic energy transfer. We provide an intuitive platform for engineering exciton transfer dynamics and we show that careful consideration of the properties of the environment leads to opportunities to engineer the transfer of an exciton. Since excitons in nanostructures are proposed for use in quantum information processing and artificial photosynthetic designs, our approach paves the way for engineering a wide range of desired exciton dy- namics. Finally, we develop the theory for a two-dimensional electronic spectroscopic technique based on fluorescence (2DFS) and challenge previous theoretical results claiming its equivalence to the two-dimensional photon echo (2DPE) technique which is based on polarization. Experimental realization of this technique confirms our the- oretical predictions. The new technique is more sensitive than 2DPE as a tool for conformational determination of excitonically coupled chromophores and o↵ers the possibility of applying two-dimensional electronic spectroscopy to single-molecules.
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Semiclassical hybrid dynamics for open quantum systemsGoletz, Christoph-Marian 20 July 2011 (has links) (PDF)
In this work the semiclassical hybrid dynamics is extended in order to be capable of treating open quantum systems considering finite baths. The corresponding phenomena, i.e. decoherence and dissipation, are investigated for various scenarios.
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Teorie relaxace a přenosu energie v otevřených kvantových systémech / Theory of Relaxation and Energy Transfer in Open Quantum SystemsOlšina, Jan January 2014 (has links)
The work summarizes basic theory of relaxation, energy transfer and decoher- ence in photosynthetic molecular aggregates described as open quantum systems and basic theory of third order coherent non-linear spectroscopy. The work presents two methods for calculation of photo-induced dynamics of molecular aggregates. The methods relax certain approximations of the theories commonly used to model the relaxation and energy transfer in the molecular systems on the sub-picosecond time scale. The first theory derived in the formalism of para- metric projection operators accounts for correlations in a second-order non-linear response-function that are usually neglected in the formalism of master equations. The second theory represents stochastic model of exact dynamics via the cumulant expansion. The work also presents an analysis of importance of the secular and the Markov approximations in the description of dynamics derived in the second-order perturbation theory in the system-bath coupling with emphasis on the excitonic coherence lifetime.
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Stabilité, dispersion, et création de paires pour certains systèmes quantiques infinis / Stability, dispersion, and pair production for some infinite quantum systemsSabin, Julien 12 December 2013 (has links)
Cette thèse est consacrée à l'étude mathématique des propriétés de stabilité de systèmes quantiques infinis, décrits par des modèles non linéaires. Dans les chapitres 1 et 2, on étudie l'instabilité du vide relativiste menant au phénomène de création de paires électron-positron. Dans le chapitre 3, on considère la dynamique de ce même vide relativiste couplé à un champ scalaire. Les chapitres 4 et 5 sont consacrés au caractère dispersif de la dynamique non linéaire de Hartree pour des perturbations de la mer de Fermi, et en particulier à sa stabilité orbitale et asymptotique. Enfin, le chapitre 6 introduit une notion générale d'entropie relative entre deux états comportant une infinité de particules. / This thesis is devoted to the mathematical study of stability properties of infinite quantum systems described by nonlinear models. In chapters 1 and 2, we study the instability of the relativistic vacuum leading to the phenomenon of electron-positron pair production. In chapter 3, we consider the dynamics of this same relativistic vacuum coupled to a scalar field. Chapters 4 and 5 are devoted to the dispersive behaviour of the nonlinear Hartree dynamics for perturbations of the Fermi sea, and in particular to its orbital and asymptotic stability. Finally, chapter 6 introduces a general notion of relative entropy between states having infinitely many particles.
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Invariantes dinâmicos, estados coerentes e fases geométricas em mecânica quânticaLima, Dibartolomei Antônio Pereira de 08 August 2014 (has links)
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Previous issue date: 2014-08-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, we study the generalized harmonic oscillator with frequency dependent mass
and time and subjected to a friction force whose speed depends on the time, of classical
and quantum points of view. Obtained the solutions of the classical equation of motion of
this system for some special cases, we derive an equation of motion that describes three
systems. Then, with the help of quadratic invariant operators the light of the method
of dynamical invariants we find the exact solutions of the Schrodinger equation for this
system. We derive the geometric, dynamic and Berry for this system non-stationary
phases and we evaluate this phases for three special cases. After this, we construct
coherent states for this quantized system and employ them to investigate some properties
quantum properties such as quantum
uctuations of the coordinate and momentum as
well as the product of the uncertainties. We then use a linear invariant operator light of the
method of dynamical invariants in the intention of finding exact Schrodinger equation for
the damped harmonic oscillator for forced time-dependent solutions. As described in our
contribution we built solutions in the form of Gaussian wave packets as well as calculate
the quantum
uctuations of the coordinates and time, as well as the correlations between
them. Finally, we show that the width of the
uctuations and correlations of the Gaussian
packet does not depend on the external force / Na presente tese, estudamos o oscilador harmônico generalizado com massa e frequência
dependentes do tempo e submetido a uma força de fricção linear na velocidade cujo coeficiente de fricção depende do tempo, do ponto de vista clássico e quântico. Obtivemos as
soluções da equação de movimento clássica deste sistema para alguns casos particulares e
derivamos uma equação de movimento que descreve simultaneamente três sistemas diferentes.
Em seguida, com a ajuda dos operadores invariantes quadráticos e à luz do método
de invariantes dinâmicos encontramos as soluções exatas da equação de Schrodinger para
este sistema. Também derivamos as fases geométrica, dinâmica e de Berry para este
sistema não-estacionário e as avaliamos para três casos especiais. Ainda construímos estados
coerentes para este sistema quantizado e os empregamos para investigar algumas
propriedades quânticas tais como
utuações quânticas da coordenada e momento bem
como do produto das incertezas. Em seguida, utilizamos um operador invariante linear
e usamos o método de invariantes dinâmicos para encontrar soluções exatas da equação
de Schrodinger para um oscilador harmônico amortecido e forçado dependente do tempo.
Com as soluções desta equação, construímos soluções na forma de pacotes de onda Gaussianos
assim como calculamos as
utuações quânticas das coordenadas e momentos, bem
como as correlações entre ambos. Finalmente, mostramos que a largura das
utuações e
correlações do pacote Gaussiano não dependem da força externa.
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Extensão dos Be-ables de Bell e Competição Atenuação x Amplificação / Extended Bell´s Be-ables and Atenuattion × Amplification Competition.Felipe Lorenzen 16 February 2009 (has links)
Na primeira parte deste trabalho empregamos a equação estocástica de Itô para obter uma interpretação generazilada de be-ables, que engloba dissipação, decoerência e a transição da dinâmica quântica para clássica. Ao escolher uma fonte de estocasticidade que leva à correção dissipativa da dinâmica hamiltoniana na forma de Lindblad, obtemos uma nova classe de trajetórias que incorpora às trajetórias de Bohm o termo difusivo presente na formulação de Nelson. Utilizando nossa formulação extendida dos be-ables identificamos o processo de decoerência e verificamos que este encontra-se em concordância com o formalismo quântico usual. Na segunda parte deste trabalho analisamos a dinâmica de um sistema quântico sob a competição de dois sistemas multimodais contra-atuantes: um atenuador ou reservatório térmico e um amplificador de Glauber. Mapeamos o comportamento dinâmico deste sistema, identificando diferentes regimes de parâmetros. Calculamos o processo de decoerência emergente da ação dos sistemas multimodais e discutimos aplicações para o nosso sistema. Na terceira parte deste trabalho, usamos a abordagem de campo médio para a obtençãoo da equação mestra que descreve o problema da superradiância sob a ação de flutuações térmicas do reservatório. Desejamos com isso explorar a possibilidade de se verificar o processo de ressonância estocástica no âmbito da superradiância. / In the first part of this work we employ the Itô stochastic equation to extend Bells be-able interpretation of quantum mechanics to encompass dissipation, decoherence and quantum-to-classical transition through quantum trajectories. For a particular choice of the source of stochasticity, the one leading to a dissipative Lindblad type correction to the Hamiltonian dynamics, we verify that the diffusive term in Nelson´s formalism is naturally incorporated into Bohm´s one, rendering a unified Bohm-Nelson theory. Mainly, analyzing the intereference between quantum trajectories, we clearly identify the decoherence time, as estimated from the usual quantum formalism. We also observe the quantum-to-classical transition through the convergence of the infinite possible quantum trajectories to their associated classical counterparts. In the second part of this work we analyze the dynamical behavior of a quantum system under the actions of two counteracting baths: the inevitable energy draining reservoir and, oppositly, an enginereed Glauber amplifier feeding the system excitation. We trace the system dynamics towards equilibrium to mapp its distinct behaviors following from the attenuation × amplification interplay. The decoherence process emerging from the action of both counteracting baths is also computed and, finally, applications of such an attenuation × amplification competition is discussed. Finally, in the third part of this work we employ the mean field approximation to derive the master equation describing the process of superradiant emission under the presence of thermal fluctuation. We envisage to explore the possibility of observe stochastic resonance within the superradiant process.
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Quantum non-Markovianity induced by classical stochastic noise / Não-Markovianidade quântica induzida por ruído estocástico clássicoJosé Inácio da Costa Filho 26 July 2017 (has links)
One of the main goals of the theory of open quantum systems is to devise methods which help preserve the quantum properties of a system interacting with its environment. One possible pathway to achieve this goal is to use non-Markovian reservoirs, characterized by information backflows and revivals of certain quantum properties. These reservoirs usually require advanced engineering techniques, which may turn their implementation impractical. In this dissertation we propose an alternative technique: the injection of a classical colored noise, which induces the desired quantum non-Markovianity. In order to do that, we investigate the dynamics of a quantum system interacting with its surrounding environment and under the injection of a classical stochastic colored noise. A time-local master equation for the system is derived by using the stochastic wave function formalism and functional calculus. Afterwards, the non-Markovianity of the evolution is detected by using the Andersson, Cresser, Hall and Li measure, which is based on the decay rates of the master equation in canonical Lindblad-like form. Finally, we evaluate the measure for three different colored noises and study the interplay between environment and noise pump necessary to induce quantum non-Markovianity, as well as the energy balance of the system. / Um dos objetivos principais da teoria de sistemas quânticos abertos é desenvolver métodos que ajudem a preservar as propriedades quânticas de um sistema interagindo com o ambiente. Um possível caminho para alcançar essa meta é usar reservatórios não-Markovianos, caracterizados por refluxos de informação e renascimento de certas propriedades quânticas. Esses reservatóris geralmente requerem o uso de técnicas avançadas de engenharia, o que pode tornar sua implementação impraticável. Nessa dissertação nós propomos uma técnica alternativa: a injeção de um ruído colorido clássico, o qual induz a desejada não-Markovianidade quântica. De modo a fazer isso, nós investigamos a dinâmica de um sistema quântico interagindo com o ambiente e sob a injeção de um ruído colorido clássico estocástico. Uma equação mestra local no tempo é derivada usando-se do formalismo da função de onda estocástica e de técnicas de cálculo funcional. Após isso, a não-Markovianidade da evolução é detectada através da medida de Andersson, Cresser, Hall e Li, a qual é baseada nos coeficientes da equação mestra na forma de Lindblad-like canônica. Finalmente, nós calculamos a medida para três diferentes ruídos coloridos e estudamos a relação entre o ambiente e o bombeio estocástico necessária para induzir não-Markovianidade quântica, assim como o balanço de energia do sistema.
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Evolution of a 1D bipartite fermionic chain under in?uence of a phenomenological dephasingRibeiro, 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.
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Expansão perturbativa para fenômenos a tempos curtos / Perturbative expansion for short-time phenomenaRamisés Martins da Silva 27 October 2016 (has links)
Fenômenos que ocorrem a tempos curtos em sistemas quânticos abertos são caracterizados por possuírem um tempo característico de uma ordem muito menor que o tempo de relaxação do sistema. Como exemplos podemos citar o efeito de decoerência, que em resumo tenta explicar como a natureza quântica de um sistema é perdida ao longo da interação com o ambiente e o fenômeno de superradiância, onde estuda-se como alguns sistemas emitem um pulso energético muito rápido gerando um pico de intensidade fino localizado muito antes da relaxação do sistema. O objetivo desse trabalho é não só estudar esses fenômenos mas como apresentar uma técnica alternativa para a quantificação das medidas associadas e de seus tempos característicos. A técnica apresentada se baseia em fazer uma expansão perturbativa no tempo para o operador densidade a partir de uma equação mestra quântica e com seu uso calcular grandezas físicas relevantes a fenômenos que ocorrem a tempos curtos. A simplicidade da técnica e seu uso abrangente são os principais fatores motivadores deste trabalho. / Short-time phenomena in open quantum systems are characterized by having a characteristic time of a much lower order than the relaxation time of the system. As examples we can mention the effect of decoherence, which in summary tries to explain how the quantum nature of a system is lost along the interaction with the environment and the superradiance phenomenon, where is studied how some systems emit a very fast energy pulse generating a peak of fine intensity located long before the relaxation of the system. The aim of this work is not only study these phenomena but to present an alternative technique for quantifying the associated measures and their characteristic times. The presented technique is based on making a perturbative expansion in time for the density operator from a quantum master equation and use it to calculate physical quantities relevant to phenomena occurring at short times. The simplicity of the technique and its widespread use are the main motivating factors of this work.
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