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Quantum statistical mechanics
Title statement Quantum statistical mechanics : equilibrium and non-equilibrium theory from first principles / Phil Attard. [elektronický zdroj] Publication Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2015] Phys.des. 1 online resource (various pagings) : illustrations (some color). ISBN 9780750311885 (online) 9780750311908 mobi Edition [IOP release 2] IOP expanding physics, ISSN 2053-2563 Note "Version: 20151001"--Title page verso. Internal Bibliographies/Indexes Note Includes bibliographical references. Contents 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 universe Content note 2 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 oscillator. 3 Probability in quantum systems -- 3.1 Formulation of probability -- 3.2 Transitions -- 3.3 Non-equilibrium probability. 4 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 reversibility. 5 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 operator. 6 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 theory. Appendices. -- A. Probability densities and the statistical average -- B. Stochastic state transitions for a non-equilibrium system -- C. Entropy eigenfunctions, state transitions, and phase space. Notes to Availability Přístup pouze pro oprávněné uživatele Audience Upper-level undergraduate to graduate level physics and mathematics students, and academics seeking a firmer grounding in key concepts. Note Způsob přístupu: World Wide Web.. Požadavky na systém: Adobe Acrobat Reader. Another responsib. Institute of Physics (Great Britain), Subj. Headings Quantum statistics. * Equilibrium - Statistical methods. * Nonequilibrium statistical mechanics. * Statistical mechanics. * Statistical physics. * SCIENCE / Physics / Condensed Matter. Form, Genre elektronické knihy electronic books Country Anglie Language angličtina Document kind Electronic books URL Plný text pro studenty a zaměstnance UPOL 
book
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 Schrödinger equation.
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.
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