by Carolyne M Van Vliet (Université de Montréal, Canada & University of Miami, USA)

Table of Contents (67k)
Preface (114k)
Chapter 1: Introduction to the State of Large Systems and Some Probability Concepts (648k)
Chapter 2: Statistics of Closed Systems (377k)
Chapter 3: Thermodynamics in the Microcanonical Ensemble, Classical and Quantal (519k)

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.

• General Principles of Many-Particle Systems:
  • Introduction to the State of Large Systems and Some Probability Concepts
  • Statistics of Closed Systems
  • Thermodynamics in the Microcanonical Ensemble, Classical and Quantal
  • Ensembles in the Presence of Reservoirs. The Canonical and Grand-Canonical Ensemble
  • Generalized Canonical Ensembles
• Classical and Quantum Formalisms. The Boltzmann Gas, The Perfect Bose and Fermi Gas:
  • The Boltzmann Distribution and Chemical Applications
  • The Occupation-Number State Formalism; Spin and Statistics
  • Ideal Quantum Gases and Elementary Excitations in Solids
• Quantum Systems with Strong Interactions:
  • Critical Phenomena: General Features of Phase Transitions
  • Renormalization: Theory and Examples
  • The Two-Dimensional Ising Model and Spin Waves
  • Aspects of Quantum Fluids
• Classical Transport Theory:
  • The Boltzmann Equation and Boltzmann's H-Theorem
  • Hydrodynamic Equations and Conservation Theorems; Barycentric Flow
  • Further Applications
• Linear Response Theory and Quantum Transport:
  • Linear Response Theory, Reduced Operators and Convergent Forms
  • The Quantum Boltsmann Equation and Some Applications of Modified Linear Response
  • Brownian Motion and the Mesoscopic Master Equation
  • Branching Processes and Continuous Stochastic Phenomena
  • Stochastic Optical Signals and Photon Fluctuations