Equilibrium and Non-equilibrium Statistical Mechanics

Carolyne M. Van Vliet

Published by World Scientific Publishing Company, 2008
ISBN 10: 9812704787 / ISBN 13: 9789812704788
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Synopsis: This book is destined to be the standard graduate text in this fascinating field that encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response, kinetic equations and stochastic processes.

The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the micro-canonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.

In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis, the Casimir Onsager relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round.

Contents:

  • Equilibrium Statistical Mechanics:
  • General Principles of Many-Particle Systems: Probability and Generating Functions, Ensembles, Illustrations;
  • Classical and Quantum Formalisms: Occupation-Number States, Field Operators and Perfect Gases;
  • Quantum Systems with Strong Interactions: Phase Transitions, Renormalization, Aspects of Quantum Liquids and Diagrammatic Methods;
  • Non-Equilibrium Statistical Mechanics: Classical Boltzmann Transport Theory;
  • Linear Response Theory and Quantum Transport: The Original Kubo-Green Formalism, Reduced Operators and Convergent Forms, Some Applications of Modified Linear Response;
  • Stochastic Phenomena: Brownian Motion and the Mesoscopic Master Equation, Spectral Analysis, Branching Processes, Stochastic Optical Signals and Photon Fields;
  • Appendices: The Schrödinger, Heisenberg and Interaction Picture; Spin and Statistics.

Review: The text combines remarkable mathematical rigor with a well-balanced presentation of the underlying physical ideas and the ensuing conceptual framework. The author draws on many years of teaching experience and an expert career in the field, with the declared aim of offering a future standard graduate text and reference in statistical physics ... this volume should certainly become indispensable as a reference text for both lecturers and researchers. --Mathematical Reviews

The book clearly is the first-rate text on statistical mechanics. The selection of topics is well-balanced. Exciting topics are included, and the description is straightforward. Advanced mathematical tools such as second quantization, contour integrals, and Dirac perturbation theory, cluster diagrams, Feynman diagrams are introduced and used unhesitatingly. The book is at the same level as that of Jackson's book on Electrodynamics. --S Fujita, Professor, SUNY, Buffalo

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Bibliographic Details

Title: Equilibrium and Non-equilibrium Statistical ...
Publisher: World Scientific Publishing Company
Publication Date: 2008
Binding: Paperback
Book Condition: Used: Good

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Book Description World Scientific Publishing Co Pte Ltd, Singapore, 2008. Paperback. Book Condition: New. New revised ed. Language: English . Brand New Book. This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round. Bookseller Inventory # AAJ9789812704788

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Book Description World Scientific Publishing Co Pte Ltd, Singapore, 2008. Paperback. Book Condition: New. New revised ed. Language: English . Brand New Book. This book encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response theory, kinetic equations and stochastic processes. It is destined to be a standard text for graduate students, but it will also serve the specialist-researcher in this fascinating field; some more elementary topics have been included in order to make the book self-contained.The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the microcanonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications.In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behaviour and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis the Onsager-Casimir relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations in optical signals and radiation fields briefly make the round. Bookseller Inventory # AAJ9789812704788

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Book Description World Scientific Publishing Co Pte Ltd. Paperback. Book Condition: new. BRAND NEW, Equilibrium and Non-Equilibrium Statistical Mechanics (New & revised ed), Carolyn Van Vliet, This book is destined to be the standard graduate text in this fascinating field that encompasses our current understanding of the ensemble approach to many-body physics, phase transitions and other thermal phenomena, as well as the quantum foundations of linear response, kinetic equations and stochastic processes. The historical methods of J Willard Gibbs and Ludwig Boltzmann, applied to the quantum description rather than phase space, are featured. The tools for computations in the micro-canonical, canonical and grand-canonical ensembles are carefully developed and then applied to a variety of classical and standard quantum situations. After the language of second quantization has been introduced, strongly interacting systems, such as quantum liquids, superfluids and superconductivity, are treated in detail. For the connoisseur, there is a section on diagrammatic methods and applications. In the second part dealing with non-equilibrium processes, the emphasis is on the quantum foundations of Markovian behavior and irreversibility via the Pauli-Van Hove master equation. Justifiable linear response expressions and the quantum-Boltzmann approach are discussed and applied to various condensed matter problems. From this basis, the Casimir-Onsager relations are derived, together with the mesoscopic master equation, the Langevin equation and the Fokker-Planck truncation procedure. Brownian motion and modern stochastic problems such as fluctuations of the electromagnetic field briefly make the round. Bookseller Inventory # B9789812704788

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