Yes / Grothendieck's bound is used in the context of a single quantum system, in contrast to previous work which used it for multipartite entangled systems and the violation of Bell-like inequalities. Roughly speaking the Grothendieck theorem considers a 'classical' quadratic form ${\cal C}$ that uses complex numbers in the unit disc, and takes values less than 1. It then proves that if the complex numbers are replaced with vectors in the unit ball of the Hilbert space, then the 'quantum' quadratic form ${\cal Q}$ might take values greater than 1, up to the complex Grothendieck constant $k_\mathrm G$. The Grothendieck theorem is reformulated here in terms of arbitrary matrices (which are multiplied with appropriate normalisation prefactors), so that it is directly applicable to quantum quantities. The emphasis in the paper is in the 'Grothendieck region' $(1,k_\mathrm G)$, which is a classically forbidden region in the sense that ${\cal C}$ cannot take values in it. Necessary (but not sufficient) conditions for ${\cal Q}$ taking values in the Grothendieck region are given. Two examples that involve physical quantities in systems with six and 12-dimensional Hilbert space, are shown to lead to ${\cal Q}$ in the Grothendieck region $(1,k_\mathrm G)$. They involve projectors of the overlaps of novel generalised coherent states that resolve the identity and have a discrete isotropy.

No description available.

No / A finite quantum system in which the position and momentum take values in the Galois field GF(p¿l) is constructed from a smaller quantum system in which the position and momentum take values in Zp , using field extension. The Galois trace is used in the definition of the Fourier transform. The Heisenberg¿Weyl group of displacements and the Sp(2, GF(p¿l)) group of symplectic transformations are studied. A class of transformations inspired by the Frobenius maps in Galois fields is introduced. The relationship of this 'Galois quantum system' with its subsystems in which the position and momentum take values in subfields of GF(p¿l) is discussed.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20546号 / 理博第4304号 / 新制||理||1618(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 早川 尚男, 教授 川上 則雄, 教授 佐々 真一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24440号 / 理博第4939号 / 新制||理||1706(附属図書館) / 京都大学大学院理学研究科化学専攻 / (主査)教授 谷村 吉隆, 教授 林 重彦, 教授 鈴木 俊法 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

yes / In a quantum system with d-dimensional Hilbert space, the Q-function of a Hermitian positive semide nite operator , is de ned in terms of the d2 coherent states in this system. The Choquet integral CQ( ) of the Q-function of , is introduced using a ranking of the values of the Q-function, and M obius transforms which remove the overlaps between coherent states. It is a gure of merit of the quantum properties of Hermitian operators, and it provides upper and lower bounds to various physical quantities in terms of the Q-function. Comonotonicity is an important concept in the formalism, which is used to formalize the vague concept of physically similar operators. Comonotonic operators are shown to be bounded, with respect to an order based on Choquet integrals. Applications of the formalism to the study of the ground state of a physical system, are discussed. Bounds for partition functions, are also derived.

No description available.

Este projeto se destina ao estudo de sistemas quânticos não relativísticos de dois, quatro e oito níveis de energia que descrevem partículas com spin s=1/2 sujeitas à ação de campos externos e interagentes entre si. São apresentadas soluções exatas para as equações que regem esses sistemas. Tais sistemas possuem uma vasta aplicação em diversas áreas da física, dentre as quais é possível destacar a computação quântica. Possíveis aplicações dos resultados são a construção de portas lógicas quânticas universais. Estas portas lógicas quânticas representam um elemento essencial no desenvolvimento dos chamados computadores quânticos. A análise e a implementação destes computadores quânticos exige a manipulação de sistemas de vários níveis, sujeitos a campos externos dependentes do tempo. Neste trabalho é apresentada a solução para o assim chamado Problema de Rabi, um particular problema de dois níveis. Um exemplo de solução para o sistema de quatro níveis, aqui relativo a um problema de dois spins também é discutido. Foram obtidas soluções exatas para sistemas de oito níveis cuja possível aplicação é a Correção Quântica de Erros. / This project aims to study the non-relativistic quantum systems of two, four and eight energy levels that describe particles with spin s=1/2 in external .elds and interacting with each other. We find exact analitical solutions for these systems. Such systems have extensive applications in various areas of physics, among which its possible to highlight quantum computing. Possible applications of the results are the construction of quantum universal logic gates.These quantum logic gates are an essential element in the development of so-called quantum computers. The analysis and implementation of quantum computers requires handling systems of various levels, subject to time-dependent external fields. This work presents a solution to the so-called Rabi problem, a particular problem at two levels. An example of a solution to the system of four levels, related to two spins problem is also investigated. We obtained exact solutions for systems of eight levels with possible application to the Quantum Error Correction.

A Termodinâmica foi concebida através da observação da eficiência no funcionamento mecânico de máquinas que dependiam da troca de temperatura e calor com meio. O paradigma de modelo nesses estudos foram máquinas idealizadas que operavam em ciclos tais como o ciclo de Carnot (o mais eficiente possível) e o ciclo de Otto. Esses ciclos de operação das máquinas ditas térmicas podem ser decompostos em trechos em que processos termodinâmicos, tais como adiabático e isotérmico, atuam. Contudo, embora a compreensão da eficiência no funcionamento dessas máquinas tenha sido o primeiro passo, esta teoria não ficou limitada a tal, se desenvolvendo ao ponto de ser considerada um dos pilares da Física moderna. Atualmente tem-se visto um crescimento substancial dos estudos da Termodinâmica considerando sistemas pequenos e/ou fora do equilíbrio termodinâmico. Resultados curiosos têm sido obtidos quando considerados sistemas pequenos tais que efeitos quânticos têm grande relevância. Nesta situação surge o que tem sido chamado de Termodinâmica quântica: as leis da Termodinâmica sendo obtidas a partir de flutuações descritas pela Mecânica Quântica. Naturalmente, um dos primeiros problemas a ser tratado nesta nova circunstância foi a eficiência de máquinas térmicas. Para a descrição dessas máquinas quânticas foi-se primeiro construído o que seriam os diferentes processos termodinâmicos que guiam o funcionamento da mesma. Baseado nesses resultados, as versões quânticas dos ciclos de Carnot e Otto, através dos quais essas máquinas operavam, foram também determinados e as propriedades das máquinas térmicas puderam ser exploradas e comparadas com seu análogo clássico. Nesta dissertação estudaremos diferentes tipos de máquinas térmicas operando no ciclo de Otto. Essas máquinas são descritas por Hamiltonianos de dois spins 1/2 que apresentam interação. Algumas características desses Hamiltonianos são exploradas e o papel das mesmas sobre a eficiência da máquina foram determinado. Comparamos também esta eficiência com os limites dados pelo ciclo de Carnot e o limite dado pela situação em que o acoplamento entre os spins é nulo. Diferentes situações físicas são exploradas e suas consequências determinadas. Por fim, proporemos algumas discussões sobre o papel da Mecânica Quântica no funcionamento destas máquinas. / Thermodynamics was conceived by observing the efficiency of the mechanical operation of machines that depended on the temperature and heat exchange with the surroundings. The paradigm model in these studies were idealized machines operating in cycles such as the Carnot cycle (the most efficient one) and the Otto cycle. These thermal operating cycles of the machines can be decomposed into parts that thermodynamic processes, such as isothermal and adiabatic, act. However, while the understanding of efficiency in the functioning of these machines has been the first step, this theory was not limited to this, being developed the point of being considered one of the pillars of modern Physics. Currently, it has seen a substantial growth of Thermodynamics studies considering small systems and / or out of equilibrium thermodynamical systems. Curious results have been obtained when considered small systems such that quantum effects are highly relevant. In this situation arises what has been called quantum thermodynamics: the laws of thermodynamics being derived from fluctuations described by Quantum Mechanics. Of course, one of the problems to be addressed in the new condition was the efficiency of heat engines. For a description of these quantum machines first was built what would be the different thermodynamical processes that guide the operation. Based on these results, the quantum versions of Carnot and Otto cycles, through which these machines operate, were also determined and the properties of thermal machines could be explored and compared with its classical analog. This thesis will study different types of heat engines operating in Otto cycle. Such machines are described by two spin 1/2 Hamiltonian presenting interaction. Some characteristics of these Hamiltonians are explored and the role of them on the machine efficiency were determined. We also compared this efficiency with the limits given by the Carnot cycle and the limit given by the situation which the coupling between the spins is zero. Different physical situations are explored and its consequences determined. Finally, we propose some discussions about the role of quantum mechanics in the operation of these machines.

Understanding energy transfer at the molecular scale is both essential for the design of novel molecular level devices and vital for uncovering the fundamental properties of non-equilibrium open quantum systems. In this thesis, we first establish the connection between molecular scale devices -- molecular electronics and phononics -- and open quantum system models. We then develop theoretical tools to study various properties of these models. We extend the standard master equation method to calculate the steady state thermal current and conductance coefficients. We then study the scaling laws of the thermal current with molecular chain size and energy, and apply this tool to investigate the onset of nonlinear thermal current - temperature characteristics, thermal rectification and negative differential conductance. Our master equation technique is valid in the ``on-resonance" regime, referring to the situation in which bath modes in resonance with the subsystem modes are thermally populated. In the opposite ``off-resonance" limit, we develop the Energy Transfer Born-Oppenheimer method to obtain the thermal current scaling without the need to solve for the subsystem dynamics. Finally, we develop a mapping scheme that allows the dynamics of a class of open quantum systems containing coupled subsystems to be treated by considering the separate dynamics in different subsections of the Hilbert space. We combine this mapping scheme with path integral numerical simulations to explore the rich phenomenon of entanglement dynamics within a dissipative two-qubit model. The formalisms developed in this thesis could be applied for the study of energy transfer in different realizations, including molecular electronic junctions, donor-acceptor molecules, artificial solid state qubits and cold-atom lattices.