Formulation Of Statistical Mechanics Based On Thermal Pure Quantum States
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Formulation Of Statistical Mechanics Based On Thermal Pure Quantum States
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Author : Sho Sugiura
language : en
Publisher: Springer
Release Date : 2017-10-05
Formulation Of Statistical Mechanics Based On Thermal Pure Quantum States written by Sho Sugiura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-05 with Science categories.
This thesis introduces the concept of "thermal pure quantum (TPQ) states", which are pure quantum states in equilibrium. The author establishes a new formulation of statistical mechanics based on the TPQ states. This formulation allows us to obtain not only mechanical variables but also thermodynamic variables such as entropy and free energy from a single TPQ state. Furthermore, the formulation provides a new physical description in which all fluctuations including thermally driven ones are uniquely identified to be quantum fluctuations. The use of TPQ formulation has practical advantages in its application to numerical computations and allows for significant reduction in computation cost in numerics. For demonstration purposes, a numerical computation based on TPQ formulation is applied to a frustrated two-dimensional quantum spin model, and the result is also included in this book.
Physics Mathematics And All That Quantum Jazz
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Author : Shu Tanaka
language : en
Publisher: World Scientific
Release Date : 2014-04-01
Physics Mathematics And All That Quantum Jazz written by Shu Tanaka and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-01 with Science categories.
This book is a collection of contributions from a Summer Workshop on “Physics, Mathematics, and All That Quantum Jazz”. Subjects of the symposium include quantum information theory, quantum annealing, Bose gases, and thermodynamics from a viewpoint of quantum physics. Contributions to this book are prepared in a self-contained manner so that readers with a modest background may understand the subjects.
Equilibrium Statistical Physics
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Author : Michael Plischke
language : en
Publisher: World Scientific
Release Date : 1994
Equilibrium Statistical Physics written by Michael Plischke and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
This textbook concentrates on modern topics in statistical physics with an emphasis on strongly interacting condensed matter systems. The book is self-contained and is suitable for beginning graduate students in physics and materials science or undergraduates who have taken an introductory course in statistical mechanics. Phase transitions and critical phenomena are discussed in detail including mean field and Landau theories and the renormalization group approach. The theories are applied to a number of interesting systems such as magnets, liquid crystals, polymers, membranes, interacting Bose and Fermi fluids; disordered systems, percolation and spin of equilibrium concepts are also discussed. Computer simulations of condensed matter systems by Monte Carlo-based and molecular dynamics methods are treated.
Quantum Mathematical Physics
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Author : Felix Finster
language : en
Publisher: Birkhäuser
Release Date : 2016-02-24
Quantum Mathematical Physics written by Felix Finster and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-24 with Science categories.
Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.
Open Quantum Systems Iii
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Author : Stéphane Attal
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-07
Open Quantum Systems Iii written by Stéphane Attal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-07 with Mathematics categories.
Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. From a mathematical point of view, it involves a large body of knowledge. Significant progress in the understanding of such systems has been made during the last decade. These books present in a self-contained way the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications. In Volume I the Hamiltonian description of quantum open systems is discussed. This includes an introduction to quantum statistical mechanics and its operator algebraic formulation, modular theory, spectral analysis and their applications to quantum dynamical systems. Volume II is dedicated to the Markovian formalism of classical and quantum open systems. A complete exposition of noise theory, Markov processes and stochastic differential equations, both in the classical and the quantum context, is provided. These mathematical tools are put into perspective with physical motivations and applications. Volume III is devoted to recent developments and applications. The topics discussed include the non-equilibrium properties of open quantum systems, the Fermi Golden Rule and weak coupling limit, quantum irreversibility and decoherence, qualitative behaviour of quantum Markov semigroups and continual quantum measurements.
Thermodynamics Of Information Processing In Small Systems
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Author : Takahiro Sagawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-14
Thermodynamics Of Information Processing In Small Systems written by Takahiro Sagawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-14 with Science categories.
This thesis presents a general theory of nonequilibrium thermodynamics for information processing. Ever since Maxwell's demon was proposed in the nineteenth century, the relationship between thermodynamics and information has attracted much attention because it concerns the foundation of the second law of thermodynamics. From the modern point of view, Maxwell's demon is formulated as an information processing device that performs measurement and feedback at the level of thermal fluctuations. By unifying information theory, measurement theory, and the recently developed theory of nonequilibrium statistical mechanics, the author has constructed a theory of "information thermodynamics," in which information contents and thermodynamic variables are treated on an equal footing. In particular, the maximum work that can be extracted by the demon and the minimum work that is needed for measurement and information erasure by the demon has been determined. Additionally, generalizations of nonequilibrium relations such as a Jarzynski equality for classical stochastic systems in the presence of feedback control have been derived. One of the generalized equalities has recently been verified experimentally by using sub-micron colloidal particles. The results obtained serve as fundamental principles for information processing in small thermodynamic systems, and are applicable to nanomachines and nanodevices.
Thermal Physics
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Author : Robert Floyd Sekerka
language : en
Publisher: Elsevier
Release Date : 2015-08-19
Thermal Physics written by Robert Floyd Sekerka and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Science categories.
In Thermal Physics: Thermodynamics and Statistical Mechanics for Scientists and Engineers, the fundamental laws of thermodynamics are stated precisely as postulates and subsequently connected to historical context and developed mathematically. These laws are applied systematically to topics such as phase equilibria, chemical reactions, external forces, fluid-fluid surfaces and interfaces, and anisotropic crystal-fluid interfaces. Statistical mechanics is presented in the context of information theory to quantify entropy, followed by development of the most important ensembles: microcanonical, canonical, and grand canonical. A unified treatment of ideal classical, Fermi, and Bose gases is presented, including Bose condensation, degenerate Fermi gases, and classical gases with internal structure. Additional topics include paramagnetism, adsorption on dilute sites, point defects in crystals, thermal aspects of intrinsic and extrinsic semiconductors, density matrix formalism, the Ising model, and an introduction to Monte Carlo simulation. Throughout the book, problems are posed and solved to illustrate specific results and problem-solving techniques. - Includes applications of interest to physicists, physical chemists, and materials scientists, as well as materials, chemical, and mechanical engineers - Suitable as a textbook for advanced undergraduates, graduate students, and practicing researchers - Develops content systematically with increasing order of complexity - Self-contained, including nine appendices to handle necessary background and technical details
Quantum Mechanics
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Author : Horatiu Nastase
language : en
Publisher: Cambridge University Press
Release Date : 2022-08-04
Quantum Mechanics written by Horatiu Nastase and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-04 with Science categories.
A comprehensive, modern description of Quantum Mechanics at the graduate level, focused on developing the formalism and its applications.
Asymptotic Theory Of Quantum Statistical Inference Selected Papers
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Author : Masahito Hayashi
language : en
Publisher: World Scientific
Release Date : 2005-02-21
Asymptotic Theory Of Quantum Statistical Inference Selected Papers written by Masahito Hayashi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-02-21 with Science categories.
Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.
Computational Statistical Mechanics
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Author : W.G. Hoover
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Computational Statistical Mechanics written by W.G. Hoover and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
Computational Statistical Mechanics describes the use of fast computers to simulate the equilibrium and nonequilibrium properties of gases, liquids, and solids at, and away from equilibrium. The underlying theory is developed from basic principles and illustrated by applying it to the simplest possible examples. Thermodynamics, based on the ideal gas thermometer, is related to Gibb's statistical mechanics through the use of Nosé-Hoover heat reservoirs. These reservoirs use integral feedback to control temperature. The same approach is carried through to the simulation and analysis of nonequilibrium mass, momentum, and energy flows. Such a unified approach makes possible consistent mechanical definitions of temperature, stress, and heat flux which lead to a microscopic demonstration of the Second Law of Thermodynamics directly from mechanics. The intimate connection linking Lyapunov-unstable microscopic motions to macroscopic dissipative flows through multifractal phase-space structures is illustrated with many examples from the recent literature. The book is well-suited for undergraduate courses in advanced thermodynamics, statistical mechanic and transport theory, and graduate courses in physics and chemistry.