统计物理学方法 英文版
作者：Tomoyasu Tanaka 著
出版时间：2003年版
内容简介
This book may be used as a textbook for the first or second year graduate student who is studying concurrently such topics as theory of complex analysis， classical mechanics， classical electrodynamics， and quantum mechanics. In a textbook on statistical mechanics， it is common practice to deal with two im-portant areas of the subject： mathematical formulation of the distribution laws of sta- tistical mechanics， and demonstrations of the applicability of statistical mechanics.本书为英文版。
目录
Preface
Acknowledgements
1 The laws of thermodynamics
1.1 The thermodynamic system and processes
1.2 The zeroth law of thermodynamics
1.3 The thermal equation of state
1.4 The classical ideal gas
1.5 The quasistatic and reversible processes
1.6 The first law of thermodynamics
1.7 The heat capacity
1.8 The isothermal and adiabatic processes
1.9 The enthalpy
1.10 The second law of thermodynamics
1.11 The Carnot cycle
1.12 The thermodynamic temperature
1.13 The Camot cycle of an ideal gas
1.14 The Clausius inequality
1.15 The entropy
1.16 General integrating factors
1.17 The integrating factor and cyclic processes
1.18 Hansen\’\’s cycle
1.19 Employment of the second law of thermodynamics
1.20 The universal integrating factor
Exercises
2 Thermodynamic relations
2.1 Thermodynamic potentials
2.2 Maxwell relations
2.3 The open system
2.4 The Clausius-Clapeyron equation
2.5 The van der Waals equation
2.6 The grand potential
Exercises
3 The ensemble theory
3.1 Microstate and macrostate
3.2 Assumption of equal a priori probabilities
3.3 The number of microstates
3.4 The most probable distribution
3.5 The Gibbs paradox
3.6 Resolution of the Gibbs paradox: quantum ideal gases
3.7 Canonical ensemble
3.8 Thermodynamic relations
3.9 Open systems
3.10 The grand canonical distribution
3.11 The grand partition function
3.12 The ideal quantum gases
Exercises
4 System Hamiltonians
4.1 Representations of the state vectors
4.2 The unitary transformation
4.3 Representations of operators
4.4 Number representation for the harmonic oscillator
4.5 Coupled oscillators: the linear chain
4.6 The second quantization for bosons
4.7 The system of interacting fermions
4.8 Some examples exhibiting the effect of Fermi-Dirac statistics
4.9 The Heisenberg exchange Hamiltonian
4.10 The electron-phonon interaction in a metal
4.11 The dilute Bose gas
4.12 The spin-wave Hamiltonian
Exercises
5 The density matrix
5.1 The canonical partition function
5.2 The trace invariance
5.3 The perturbation expansion
5.4 Reduced density matrices
5.5 One-site and two-site density matrices
5.6 The four-site reduced density matrix
5.7 The probability distribution functions for the Ising model
Exercises
6 The cluster variation method
6.1 The variational principle
6.2 The cumulant expansion
6.3 The cluster variation method
6.4 The mean-field approximation
6.5 The Bethe approximation
6.6 Four-site approximation
6.7 Simplified cluster variation methods
6.8 Correlation function formulation
6.9 The point and pair approximations in the CFF
6.10 The tetrahedron approximation in the CFF
Exercises
7 Infinite-series representations of correlation functions
7.1 Singularity of the correlation functions
7.2 The classical values of the critical exponent
7.3 An infinite-series representation of the partition function
7.4 The method of Pade approximants
7.5 Infinite-series solutions of the cluster variation method
7.6 High temperature specific heat
7.7 High temperature susceptibility
7.8 Low temperature specific heat
7.9 Infinite series for other correlation functions
Exercises
8 The extended mean-field approximation
8.1 The Wentzel criterion
8.2 The BCS Hamiltonian
8.3 The s-d interaction
8.4 The ground state of the Anderson model
8.5 The Hubbard model
8.6 The first-order transition in cubic ice
Exercises
9 The exact Ising lattice identities
9.1 The basic generating equations
9.2 Linear identities for odd-number correlations
9.3 Star-triangle-type relationships
9.4 Exact solution on the triangular lattice
9.5 Identities for diamond and simple cubic lattices
9.6 Systematic naming of correlation functions on the lattice
Exercises
10 Propagation of short range order
10.1 The radial distribution function
10.2 Lattice structure of the superionic conductor AgI
10.3 The mean-field approximation
10.4 The pair approximation
10.5 Higher order correlation functions
10.6 Oscillatory behavior of the radial distribution function
10.7 Summary
11 Phase transition of the two-dimensional Ising model
11.1 The high temperature series expansion of the partition function
11.2 The Pfaffian for the Ising partition function
11.3 Exact partition function
11.4 Critical exponents
Exercises
Appendix 1 The gamma function
Appendix 2 The critical exponent in the tetrahedron approximation
Appendix 3 Programming organization of the cluster variation method
Appendix 4 A unitary transformation applied to the Hubbard Hamiltonian
Appendix 5 Exact Ising identities on the diamond lattice
References
Bibliography
Index