统计力学 第3版

preface to the third edition
preface to the second edition
preface to the first edition
historical introduction
1. the statistical basis of thermodynamics
　1.1. the macroscopic and the microscopic states
　1.2. contact between statistics and thermodynamics:physical
significance of the number (n, v,e)
　1.3. further contact between statistics and thermodynamics
　1.4. the classical ideal gas
　1.5. the entropy of mixing and the gibbs paradox
　1.6. the “correct” enumeration of the microstates
　problems
2. elements of ensemble theory
　2.1. phase space of a classical system
　2.2. liouville’s theorem and its consequences
　2.3. the microcanordcal ensemble
　2.4. examples
　2.5. quantum states and the phase space
　problems
3. the canonical ensemble
　3.1. equilibrium between a system and a heat reservoir
　3.2. a system in the canonical ensemble
　3.3. physical significance of the various statistical quantities
in the canonical ensemble
　3.4. alternative expressions for the partition function
　3.5. the classical systems
　3.6. energy fluctuations in the canonical ensemble:correspondence
with the microcanonical ensemble
　3.7. two theorems – the “equipartition” and the “virial”
　3.8. a system of harmonic oscillators
　3.9. the statistics of paramagnetism
　3.10. thermodynamics of magnetic systems:negative
temperatures
　problems
4. the grand canonical ensemble
　4.1. equilibrium between a system and a particle-energy
reservoir
　4.2. a system in the grand canonical ensemble
　4.3. physical significance of the various statistical
quantities
　4.4. examples
　4.5. density and energy fluctuations in the grand canonical
ensemble: correspondence with other ensembles
　4.6. thermodynamic phase diagrams
　4.7. phase equilibrium and the clausius-clapeyron equation
　problems
5. formulation of quantum statistics
　5.1. quantum-mechanical ensemble theory:the density matrix
　5.2. statistics of the various ensembles
　5.3. examples
　5.4. systems composed of indistinguishable particles
　5.5. the density matrix and the partition function of a system of
free particles
　problems
6. the theory of simple gases
　6.1. an ideal gas in a quantum-mechanical microcanonical
ensemble
　6.2. an ideal gas in other quantum-mechanical ensembles
　6.3. statistics of the occupation numbers
　6.4. kinetic considerations
　6.5. gaseous systems composed of molecules with internal
motion
　6.6. chemical equilibrium problems
7. ideal bose systems
　7.1. thermodynamic behavior of an ideal bose gas
　7.2. bose-einstein condensation in ultracold atomic gases
　7.3. thermodynamics of the blackbody radiation
　7.4. the field of sound waves
　7.5. inertial density of the sound field
　7.6. elementary excitations in liquid helium ii
　problems
8. ideal fermi systems
　8.1. thermodynamic behavior of an ideal fermi gas
　8.2. magnetic behavior of an ideal fermi gas
　8.3. the electron gas in metals
　8.4. ultracold atomic fermi gases
　8.5. statistical equilibrium of white dwarf stars
　8.6. statistical model of the atom
　problems
9. thermodynamics of the early universe
　9.1. observational evidence of the big bang
　9.2. evolution of the temperature of the universe
　9.3. relativistic electrons, positrons, and neutrinos
　9.4. neutron fraction
　9.5. annihilation of the positrons and electrons
　9.6. neutrino temperature
　9.7. primordial nucleosynthesis
　9.8. recombination
　9.9. epilogue
　problems
10. statistical mechanics of interacting systems:the method of
cluster expansions
　10.1. cluster expansion for a classical gas
　10.2. virial expansion of the equation of state
　10.3. evaluation of the virial coefficients
　10.4. general remarks on cluster expansions
　10.5. exact treatment of the second virial coefficient
　10.6. cluster expansion for a quantum-mechanical system
　10.7. correlations and scattering
　problems
11. statistical mechanics of interacting systems:the method of
quantized fields
　11.1. the formalism of second quantization
　11.2. low-temperature behavior of an imperfect bose gas
　11.3. low-lying states of an imperfect bose gas
　11.4. energy spectrum of a bose liquid
　11.5. states with quantized circulation
　11.6. quantized vortex rings and the breakdown of
superfluidity
　11.7. low-lying states of an imperfect fermi gas
　11.8. energy spectrum of a fermi liquid: landau’s phenomenological
theory
　11.9. condensation in fermi systems
　problems
12. phase transitions: criticality, universality, and scaling
　12.1. general remarks on the problem of condensation
　12.2. condensation of a van der waals gas
　12.3. a dynamical model of phase transitions
　12.4. the lattice gas and the binary alloy
　12.5. ising model in the zeroth approximation
　12.6. ising model in the first approximation
　12.7. the critical exponents
　12.8. thermodynamic inequalities
　12.9. landau’s phenomenological theory
　12.10. scaling hypothesis for thermodynamic functions
　12.11. the role of correlations and fluctuations
　12.12. the critical exponents v and
　12.13. a final look at the mean field theory
　problems
13. phase transitions: exact (or almost exact) results for various
models
　13.1. one-dimensional fluid models
　13.2. the ising model in one dimension
　13.3. the n-vector models in one dimension
　13.4. the ising model in two dimensions
　13.5. the spherical model in arbitrary dimensions
　13.6. the ideal bose gas in arbitrary dimensions
　13.7. other models
　problems
14. phase transitions: the renormalization group approach
　14.1. the conceptual basis of scaling
　14.2. some simple examples of renormalization
　14.3. the renormalization group: general formulation
　14.4. applications of the renormalization group
　14.5. finite-size scaling
　problems
15. fluctuations and nonequilibrium statistical mechanics
　15.1. equilibrium thermodynamic fluctuations
　15.2. the einstein-smoluchowski theory of the brownian
motion
　15.3. the langevin theory of the brownian motion
　15.4. approach to equilibrium: the fokker-planck equation
　15.5. spectral analysis of fluctuations: the wiener-khintchine
theorem
　15.6. the fluctuation-dissipation theorem
　15.7. the onsager relations
　problems
16. computer simulations
　16.1. introductionand statistics
　16.2. monte carlo simulations
　16.3. molecular dynamics
　16.5. computer simulation caveats
　problems
　appendices
　a. influence of boundary conditions on the distribution of quantum
states
　b. certain mathematical functions
　c. “volume” and “surface area” of an n-dimensional sphere of
radius r
　d. on bose-einstein functionse. on fermi-dirac functions
　f. a rigorous analysis of the ideal bose gas and the onset of
bose-einstein condensation
　g. on watson functions
　h. thermodynamic relationships
　i. pseudorandom numbers
　bibliography
　index