Equilibrium and Non-equilibrium Statistical Mechanics

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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 SchrxC3;xB6;dinger, Heisenberg and Interaction Picture; Spin and Statistics.