Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2017-09-06T20:06:39Z No. of bitstreams: 2 Dissertação - Eyber Domingos Alves - 2017.pdf: 1596313 bytes, checksum: 2ffb88a81908854702bc08bc1c29eacb (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-09-15T15:33:07Z (GMT) No. of bitstreams: 2 Dissertação - Eyber Domingos Alves - 2017.pdf: 1596313 bytes, checksum: 2ffb88a81908854702bc08bc1c29eacb (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-09-15T15:33:07Z (GMT). No. of bitstreams: 2 Dissertação - Eyber Domingos Alves - 2017.pdf: 1596313 bytes, checksum: 2ffb88a81908854702bc08bc1c29eacb (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-08-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work a description of the interaction between electromagnetic radiation and matter will be made. Two and three-level atomic systems will be addressed, which in turn is in the (Lambda) configuration.We will use the Dicke states to calculate the transition probability between the energetic levels for a 2-level ensemble of atoms interacting with a circularly polarized field. We will deduce the master equation for a two-level atom interacting with a thermal reservoir, observing the effects of irreversible spontaneous decay and loss of coherence between quantum states. Finally, we will study the phenomenon of Electromagnetically Induced Transparency (EIT) and Dark states. / Neste trabalho será feita uma descrição da interação entre a radiação eletromagnética com a matéria. Serão abordados sistemas atômicos de dois e três níveis, esse por sua vez estando na configuração (Lambda). Usaremos os estados de Dicke para calcular as probabilidades de transição entre os níveis energéticos para um ensemble de átomos de 2 níveis interagindo com um campo circularmente polarizado. Deduziremos a equação mestra para um átomo de dois níveis interagindo com um reservatório térmico, observando os efeitos de decaimento espontâneo irreversível e perda de coerência entre os estados quânticos. Por fim, estudaremos o fenômeno da Transparência Eletromagneticamente Induzida (EIT) e dos Estados Escuros.

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

Experimental studies have shown that the protein abundance in living cells varies from few tens to several thousands molecules per species. Molecular fluctuations roughly scale as the inverse square root of the number of molecules due to the random timing of reactions. It is hence expected that intrinsic noise plays an important role in the dynamics of biochemical networks. The Chemical Master Equation is the accepted description of these systems under well-mixed conditions. Because analytical solutions to this equation are available only for simple systems, one often has to resort to approximation methods. A popular technique is an expansion in the inverse volume to which the reactants are confined, called van Kampen's system size expansion. Its leading order terms are given by the phenomenological rate equations and the linear noise approximation that quantify the mean concentrations and the Gaussian fluctuations about them, respectively. While these approximations are valid in the limit of large molecule numbers, it is known that physiological conditions often imply low molecule numbers. We here develop systematic approximation methods based on higher terms in the system size expansion for general biochemical networks. We present an asymptotic series for the moments of the Chemical Master Equation that can be computed to arbitrary precision in the system size expansion. We then derive an analytical approximation of the corresponding time-dependent probability distribution. Finally, we devise a diagrammatic technique based on the path-integral method that allows to compute time-correlation functions. We show through the use of biological examples that the first few terms of the expansion yield accurate approximations even for low number of molecules. The theory is hence expected to closely resemble the outcomes of single cell experiments.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20632号 / 工博第4370号 / 新制||工||1679(附属図書館) / 京都大学大学院工学研究科分子工学専攻 / (主査)教授 佐藤 啓文, 教授 白川 昌宏, 教授 山本 量一 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

On the way to develop a complete full-band quantum transport simulation using the Pauli Master Equation, we show our present results on 1D n-i-n resistors, 1D double barrier resonant tunneling diodes (DBRTD), and 2D double-gate field effect transistors (DGFETs) using a simplified parabolic, spherical effective-mass band-structure model accounting for nonpolar scattering with acoustic (elastic) and optical (inelastic) silicon-like phonons. We also consider the effect of point-like dopants on the access resistance of thin-body double gate devices.

No description available.

No description available.

Indiana University-Purdue University Indianapolis (IUPUI) / Open quantum systems have become a rapidly developing sector for research. Such systems present novel physical phenomena, such as topological chirality, enhanced sensitivity, and unidirectional invisibility resulting from both their non-equilibrium dynamics and the presence of exceptional points. We begin by introducing the core features of open systems governed by non-Hermitian Hamiltonians, providing the PT -dimer as an illustrative example. Proceeding, we introduce the Lindblad master equation which provides a working description of decoherence in quantum systems, and investigate its properties through the Decohering Dimer and periodic potentials. We then detail our preferred experimental apparatus governed by the Lindbladian. Finally, we introduce the Liouvillian, its relation to non-Hermitian Hamiltonians and Lindbladians, and through it investigate multiple properties of open quantum systems.

The chemical master equation, formulated on the Markov assumption of underlying chemical kinetics, offers an accurate stochastic description of general chemical reaction systems on the mesoscopic scale. The chemical master equation is especially useful when formulating mathematical models of gene regulatory networks and protein-protein interaction networks, where the numbers of molecules of most species are around tens or hundreds. However, solving the master equation directly suffers from the so called "curse of dimensionality" issue. This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality". Several numerical results are presented to illustrate the promises and potential problems of these new algorithms. Comparisons with other numerical methods like Monte Carlo methods are also included. Development and analysis of the linear Shepard algorithm and its variants, all of which could be used for high dimensional scattered data interpolation problems, are also included here, as a candidate to help solve the master equation by building surrogate models in high dimensions. / Ph. D.

Esta dissertação discutirá, com uma abordagem predominantemente analítica, aspectos em aberto do Modelo Sznajd e de algumas de suas variantes. Apresentaremos uma equação mestra que descreve a evolução de opiniões para o modelo e estudaremos seus estados estacionários numa aproximação de campo médio. Mostraremos que esta simples abordagem é suficientemente para descrever seu comportamento qualitativo. A introdução de ruído à dinâmica do modelo também é analisada. Observa-se, neste caso, a existência de uma transição de fase entre um estado onde há um candidato majoritário (estado ordenado) e um estado onde todas as opiniões coexistem com aproximadamente o mesmo número de eleitores (estado desordenado), dependendo da intensidade desse ruído. Resultados de simulações de Monte Carlo numa rede de Barabási-Albert apresentam boa concordância quando confrontadas com resultados analíticos. / This work discusses, mainly with an analytical approach, the Sznajd Model and some of its variants. We propose a master equation that describes the evolution of opinions in the model, studying its possible steady states in a mean-field approximation. We show that this approach, although very simple, is enough to describe the qualitative behavior of the model. The introduction of noise in the dynamics is also studied in detail. In this case we show that there is a phase transition between an state in which a single candidate has the majority of the votes (ordered phase) and another one where the votes are well distributed among all the candidates (disordered phase), depending on the level of noise. Monte Carlo simulations in a Barabási-Albert network show good agreement with the analytical results.