Statistical Mechanics

Front Cover
Academic Press, Apr 6, 2011 - Psychology - 744 pages

Statistical Mechanics explores the physical properties of matter based on the dynamic behavior of its microscopic constituents. After a historical introduction, this book presents chapters about thermodynamics, ensemble theory, simple gases theory, Ideal Bose and Fermi systems, statistical mechanics of interacting systems, phase transitions, and computer simulations.

This edition includes new topics such as BoseEinstein condensation and degenerate Fermi gas behavior in ultracold atomic gases and chemical equilibrium. It also explains the correlation functions and scattering; fluctuationdissipation theorem and the dynamical structure factor; phase equilibrium and the Clausius-Clapeyron equation; and exact solutions of one-dimensional fluid models and two-dimensional Ising model on a finite lattice. New topics can be found in the appendices, including finite-size scaling behavior of Bose-Einstein condensates, a summary of thermodynamic assemblies and associated statistical ensembles, and pseudorandom number generators. Other chapters are dedicated to two new topics, the thermodynamics of the early universe and the Monte Carlo and molecular dynamics simulations.

This book is invaluable to students and practitioners interested in statistical mechanics and physics.

  • Bose-Einstein condensation in atomic gases
  • Thermodynamics of the early universe
  • Computer simulations: Monte Carlo and molecular dynamics
  • Correlation functions and scattering
  • Fluctuation-dissipation theorem and the dynamical structure factor
  • Chemical equilibrium
  • Exact solution of the two-dimensional Ising model for finite systems
  • Degenerate atomic Fermi gases
  • Exact solutions of one-dimensional fluid models
  • Interactions in ultracold Bose and Fermi gases
  • Brownian motion of anisotropic particles and harmonic oscillators
 

Contents

Chapter 1 The Statistical Basis of Thermodynamics
1
Chapter 2 Elements of Ensemble Theory
25
Chapter 3 The Canonical Ensemble
39
Chapter 4 The Grand Canonical Ensemble
91
Chapter 5 Formulation of Quantum Statistics
115
Chapter 6 The Theory of Simple Gases
141
Chapter 7 Ideal Bose Systems
179
Chapter 8 Ideal Fermi Systems
231
The Method of Quantized Fields
345
Criticality Universality and Scaling
401
Exact or Almost Exact Results for Various Models
471
The Renormalization Group Approach
539
Chapter 15 Fluctuations and Nonequilibrium Statistical Mechanics
583
Chapter 16 Computer Simulations
637
Appendices
653
Bibliography
687

Chapter 9 Thermodynamics of the Early Universe
275
The Method of Cluster Expansions
299

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About the author (2011)

Paul D. Beale is a Professor of Physics at the University of Colorado Boulder. He earned a B.S. in Physics with Highest Honors at the University of North Carolina Chapel Hill in 1977, and Ph.D. in Physics from Cornell University in 1982. He served as a postdoctoral research associate at the Department of Theoretical Physics at Oxford University from 1982-1984. He joined the faculty of the University of Colorado Boulder in 1984 as an assistant professor, was promoted to associate professor in 1991, and professor in 1997. He served as the Chair of the Department of Physics from 2008-2016. He also served as Associate Dean for Natural Sciences in the College of Arts and Sciences, and Director of the Honors Program. He is currently Director of the Buffalo Bicycle Classic, the largest scholarship fundraising event in the State of Colorado. Beale is a theoretical physicist specializing in statistical mechanics, with emphasis on phase transitions and critical phenomena. His work includes renormalization group methods, finite-size scaling in spin models, fracture modes in random materials, dielectric breakdown in metal-loaded dielectrics, ferroelectric switching dynamics, exact solutions of the finite two-dimensional Ising model, solid-liquid phase transitions of molecular systems, and ordering in layers of molecular dipoles. His current interests include scalable parallel pseudorandom number generators, and interfacing quantum randomness with cryptographically secure pseudorandom number generators. He is coauthor with Raj Pathria of the third and fourth editions of the graduate physics textbook Statistical Mechanics. The Boulder Faculty Assembly has honored him with the Excellence in Teaching and Pedagogy Award, and the Excellence in Service and Leadership Award. Beale is a private pilot and an avid cyclist. He is married to Erika Gulyas, and has two children: Matthew and Melanie.

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