Quantum statistical mechanics :equilibrium and non-equilibrium theory from first principles /

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"Version: 20151001"--Title page verso.Includes bibliographical references.Preface -- Author biography -- 1 Probability operator and statistical averages -- 1.1 Expectation, density operator and averages -- 1.2 Uniform weight density of wave space -- 1.3 Canonical equilibrium system -- 1.4 Environmental selection -- 1.5 Wave function collapse and the classical universe2 Examples and applications : equilibrium -- 2.1 Bosons, fermions and wave function symmetry -- 2.2 Ideal quantum gas -- 2.3 State occupancy by ideal particles -- 2.4 Thermodynamics and statistical mechanics of ideal particles -- 2.5 Classical ideal gas -- 2.6 Ideal Bose gas -- 2.7 Ideal Fermi gas -- 2.8 Simple harmonic oscillator3 Probability in quantum systems -- 3.1 Formulation of probability -- 3.2 Transitions -- 3.3 Non-equilibrium probability4 Time propagator for an open quantum system -- 4.1 Adiabatic time propagator -- 4.2 Stochastic time propagator -- 4.3 Kraus representation and Lindblad equation -- 4.4 Caldeira-Leggett model -- 4.5 Time correlation function -- 4.6 Transition probability -- 4.7 Microscopic reversibility5 Evolution of the canonical equilibrium system -- 5.1 Transitions between entropy states -- 5.2 Second entropy for transitions -- 5.3 Trajectory in wave space -- 5.4 Time derivative of entropy operator6 Probability operator for non-equilibrium systems -- 6.1 Entropy operator for a trajectory -- 6.2 Point entropy operator -- 6.3 Non-equilibrium probability operator -- 6.4 Approximations for the dynamic entropy operator -- 6.5 Perturbation of the non-equilibrium probability operator -- 6.6 Linear response theoryAppendices. -- A. Probability densities and the statistical average -- B. Stochastic state transitions for a non-equilibrium system -- C. Entropy eigenfunctions, state transitions, and phase space.This book establishes the foundations of non-equilibrium quantum statistical mechanics in order to support students and academics in developing and building their understanding. The formal theory is derived from first principles by mathematical analysis, with concrete physical interpretations and worked examples throughout. It explains the central role of entropy; it's relation to the probability operator and the generalisation to transitions, as well as providing first principles derivation of the von Neumann trace form, the Maxwell-Boltzmann form and the Schr?odinger equation.Upper-level undergraduate to graduate level physics and mathematics students, and academics seeking a firmer grounding in key concepts.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader.Phil Attard is a research scientist working broadly in the areas of statistical mechanics, thermodynamics, and colloid and surface science. He has held academic positions at various universities in Australia, Europe and North America, and he was a Professorial Research Fellow of the Australian Research Council. He has authored some 120 papers, 10 review articles and three books, with over 5000 citations. As an internationally recognized researcher he has made seminal contributions to the theory of electrolytes and the electric double layer, to measurement techniques for atomic force microscopy and particle interactions, and to computer simulation and integral equation algorithms for condensed matter. Attard is perhaps best known for his discovery of nanobubbles and for his role in establishing their nature. In recent years his research has been focused on non-equilibrium thermodynamics and statistical mechanics. He has identified a new type of entropy-the second entropy-as the variational principle for non-equilibrium thermodynamics, and he has derived the general form of the non-equilibrium probability distribution for statistical mechanics. The theory provides a coherent approach to non-equilibrium systems and irreversible processes, and a number of things have been derived from it, including the hydrodynamic transport equations, convective heat flow pattern formation, Onsager reciprocal relations, Green-Kubo relations, linear response theory, Langevin theory, and fluctuation-dissipation and work theorems. The theory also led to the development of stochastic molecular dynamics and non-equilibrium Monte Carlo computer simulation algorithms. Attard advocates the understanding of entropy as a physical weight and the formulation of probability in terms of set theory. This unique perspective forms the basis for this and his other two books.Title from PDF title page (viewed on November 1, 2015).

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Publisher

: .,

Collation

1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750311885

Classification

530.13/3

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-

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-

Edition

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Subject(s)

Statistical mechanics.
SCIENCE / Physics / Condensed Matter.
Quantum statistics.
Equilibrium
Nonequilibrium statistical mechanics.
Statistical physics.

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Statement of Responsibility

Phil Attard.

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