Statistical Mechanics and Applications in Condensed Matter

Carlo Di Castro, Roberto Raimondi

• Publisher: Cambridge University Press
• Year: 2015
• Print ISBN:
  9781107039407
• eBook ISBN:
  9781316354988
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This innovative and modular textbook combines classical topics in thermodynamics, statistical mechanics and many-body theory with the latest developments in condensed matter physics research. Written by internationally renowned experts and logically structured to cater for undergraduate and postgraduate students and researchers, it covers the underlying theoretical principles and includes numerous problems and worked examples to put this knowledge into practice. Three main streams provide a framework for the book; beginning with thermodynamics and classical statistical mechanics, including mean field approximation, fluctuations and the renormalization group approach to critical phenomena. The authors then examine quantum statistical mechanics, covering key topics such as normal Fermi and Luttinger liquids, superfluidity and superconductivity. Finally, they explore classical and quantum kinetics, Anderson localization and quantum interference, and disordered Fermi liquids. Unique in providing a bridge between thermodynamics and advanced topics in condensed matter, this textbook is an invaluable resource to all students of physics.

Table of contents

• Cover
• Half title
• Title
• Copyright
• Contents
• Preface
• 1 Thermodynamics: a brief overview
• 2 Kinetics
• 3 From Boltzmann to Boltzmann--Gibbs
• 4 More ensembles
• 5 The thermodynamic limit and its thermodynamic stability
• 6 Density matrix and quantum statistical mechanics
• 7 The quantum gases
• 8 Mean-field theories and critical phenomena
• 9 Second quantization and the Hartree--Fock approximation
• 10 Linear response and the fluctuation--dissipation theorem in quantum systems: equilibrium and small deviations
• 11 Brownian motion and transport in disordered systems
• 12 Fermi liquids
• 13 The Landau theory of second order phase transitions
• 14 The Landau--Wilson model for critical phenomena
• 15 Superfluidity and superconductivity
• 16 Scaling theory
• 17 The renormalization group approach
• 18 Thermal Green functions
• 19 The microscopic foundations of Fermi liquids
• 20 The Luttinger liquid
• 21 Quantum interference effects in disordered electron systems
• Appendix A The central limit theorem
• Appendix B Some useful properties of the Euler Gamma function
• Appendix C Proof of the second theorem of Yang and Lee
• Appendix D The most probable distribution for the quantum gases
• Appendix E Fermi--Dirac and Bose--Einstein integrals
• Appendix F The Fermi gas in a uniform magnetic field: Landau diamagnetism
• Appendix G Ising and gas-lattice models
• Appendix H Sum over discreteMatsubara frequencies
• Appendix I Two-fluid hydrodynamics: a few hints
• Appendix J The Cooper problem in the theory of superconductivity
• Appendix K Superconductive fluctuation phenomena
• Appendix L Diagrammatic aspects of the exact solution of the Tomonaga--Luttinger model
• Appendix M Details on the theory of the disordered Fermi liquid
• Appendix N Answers to problems
• References
• Index