1st Edition

Problems on Statistical Mechanics

By D.A.R Dalvit, J Frastai, Ian Lawrie Copyright 1999
    283 Pages
    by CRC Press

    A thorough understanding of statistical mechanics depends strongly on the insights and manipulative skills that are acquired through the solving of problems. Problems on Statistical Mechanics provides over 120 problems with model solutions, illustrating both basic principles and applications that range from solid-state physics to cosmology. An introductory chapter provides a summary of the basic concepts and results that are needed to tackle the problems, and also serves to establish the notation that is used throughout the book. The problems themselves occupy five chapters, progressing from the simpler aspects of thermodynamics and equilibrium statistical ensembles to the more challenging ideas associated with strongly interacting systems and nonequilibrium processes. Comprehensive solutions to all of the problems are designed to illustrate efficient and elegant problem-solving techniques. Where appropriate, the authors incorporate extended discussions of the points of principle that arise in the course of the solutions. The appendix provides useful mathematical formulae.

    Review of theoretical definitions and formulae
    Notation used throughout the book

    First and second law
    Thermodynamic potentials and quantities
    Maxwell relations
    Simple thermodynamic processes

    Statistical Ensembles
    Microcanonical, canonical, and grand canonical ensembles
    Connection with thermodynamics
    Equipartition theorem
    Noninteracting gases of classical particles
    Noninteracting lattice-type systems
    Gases of molecules

    Quantum Statistics
    Statistics of indistinguishable particles, bosons, and fermions
    Density of states
    Black body radiation
    Debye's models for solids
    Bose condensation
    Fermi gas

    Interacting Systems
    Classical gases and virial coefficients
    Critical exponents in phase transitions
    Ising type models and Heisenberg modes
    Exact and mean field approaches

    Nonequilibrium Systems
    Random walk
    Markov chains
    Master equation
    Diffusion phenomena
    Boltzmann transport equation
    Relaxation time approximation

    Appendix: Useful Mathematical Formulae


    D.A.R Dalvit, J Frastai, Ian Lawrie

    "The best way to learn a skill is by active practice. This wonderful collection of statistical mechanics problems, compiled by the trio, supplies a host of interesting questions and carefully worked-out solutions. Anyone with a basic background in statistical mechanics and thermodynamics can pick up the book and start practice sessions."
    - Henrik Jeldtoft Jensen, Mathematics, Physics and Engineering