Preface ....................................................... xi
Authors ..................................................... xiii
Chapter 1 Basic Principles of Statistical Physics ............. 1
1.1 Microscopic and Macroscopic Description of States ......... 1
1.2 Basic Postulates .......................................... 2
1.3 Gibbs Ergodic Assumption .................................. 3
1.4 Gibbsian Ensembles ........................................ 4
1.5 Experimental Basis of Statistical Mechanics ............... 5
1.6 Definition of Expectation Values .......................... 6
1.7 Ergodic Principle and Expectation Values .................. 9
1.8 Properties of Distribution Functions ..................... 14
1.8.1 About Probabilities ............................... 14
1.8.2 Normalization Requirement of Distribution
Functions ......................................... 15
1.8.3 Property of Multiplicity of Distribution
Functions ......................................... 15
1.9 Relative Fluctuation of an Additive Macroscopic
Parameter ................................................ 16
1.9.1 Questions and Answers ............................. 20
1.10 Liouville Theorem ........................................ 26
1.10.1 Questions and Answers ............................. 30
1.11 Gibbs Microcanonical Ensemble ............................ 39
1.12 Microcanonical Distribution in Quantum Mechanics ......... 44
1.13 Density Matrix ........................................... 48
1.14 Density Matrix in Energy Representation .................. 51
1.15 Entropy .................................................. 56
1.15.1 Entropy of Microcanonical Distribution ............ 58
1.15.2 Exact and "Inexact" Differentials ................. 60
1.15.3 Properties of Entropy ............................. 61
Chapter 2 Thermodynamic Functions ............................ 67
2.1 Temperature .............................................. 67
2.2 Adiabatic Processes ...................................... 72
2.3 Pressure ................................................. 73
2.3.1 Questions on Stationary Distributions Functions
and Ideal Gas Statistics .......................... 75
2.4 Thermodynamic Identity ................................... 84
2.5 Laws of Thermodynamics ................................... 88
2.5.1 First Law of Thermodynamics ....................... 89
2.5.2 Second Law of Thermodynamics ...................... 91
2.6 Thermodynamic Potentials, Maxwell Relations .............. 93
2.7 Heat Capacity and Equation of State ...................... 98
2.8 Jacobian Method ......................................... 100
2.9 Joule-Thomson Process ................................... 105
2.10 Maximum Work ............................................ 109
2.11 Condition for Equilibrium and Stability in an Isolated
System .................................................. 113
2.12 Thermodynamic Inequalities .............................. 118
2.13 Third Law of Thermodynamics ............................. 121
2.13.1 Nernst Theorem ................................... 122
2.14 Dependence of Thermodynamic Functions on Number of
Particles ............................................... 124
2.15 Equilibrium in an External Force Field .................. 129
Chapter 3 Canonical Distribution ............................ 135
3.1 Gibbs Canonical Distribution ............................ 135
3.2 Basic Formulas of Statistical Physics ................... 139
3.3 Maxwell Distribution .................................... 160
3.4 Experimental Basis of Statistical Mechanics ............. 179
3.5 Grand Canonical Distribution ............................ 180
3.6 Extremum of Canonical Distribution Function ............. 185
Chapter 4 Ideal Gases ....................................... 189
4.1 Occupation Number ....................................... 189
4.2 Boltzmann Distribution .................................. 191
4.2.1 Distribution with Respect to Coordinates ......... 195
4.3 Entropy of a Nonequilibrium Boltzmann Gas ............... 196
4.4 Free Energy of the Ideal Boltzmann Gas .................. 200
4.5 Equipartition Theorem ................................... 223
4.6 Monatomic Gas ........................................... 227
4.7 Vibrations of Diatomic Molecules ........................ 231
4.8 Rotation of Diatomic Molecules .......................... 235
4.9 Nuclear Spin Effects .................................... 239
4.10 Electronic Angular Momentum Effect ...................... 244
4.11 Experiment and Statistical Ideas ........................ 245
4.11.1 Specific Heats ................................... 246
Chapter 5 Quantum Statistics of Ideal Gases ................. 247
5.1 Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac
Statistics .............................................. 247
5.2 Generalized Thermodynamic Potential for a Quantum
Ideal Gas ............................................... 248
5.3 Fermi-Dirac and Bose-Einstein Distributions ............. 249
5.4 Entropy of Nonequilibrium Fermi and Bose Gases .......... 252
5.4.1 Fermi Gas ........................................ 252
5.4.2 Bose Gas ......................................... 256
5.5 Thermodynamic Functions for Quantum Gases ............... 258
5.6 Properties of Weakly Degenerate Quantum Gases ........... 263
5.6.1 Fermi Energy ..................................... 263
5.7 Degenerate Electronic Gas at Temperature Different
from Zero ............................................... 266
5.8 Experimental Basis of Statistical Mechanics ............. 271
5.9 Application of Statistics to an Intrinsic
Semiconductor ........................................... 272
5.9.1 Concentration of Carriers ........................ 273
5.10 Application of Statistics to Extrinsic Semiconductor .... 279
5.11 Degenerate Bose Gas ..................................... 284
5.11.1 Condensation of Bose Gases ....................... 284
5.12 Equilibrium or Black Body Radiation ..................... 288
5.12.1 Electromagnetic Eigenmodes of a Cavity ........... 288
5.13 Application of Statistical Thermodynamics to
Electromagnetic Eigenmodes .............................. 294
Chapter 6 Electron Gas in a Magnetic Field .................. 305
6.1 Evaluation of Diamagnetism of a Free Electron Gas;
Density Matrix for a Free Electron Gas .................. 305
6.2 Evaluation of Free Energy ............................... 316
6.3 Application to a Degenerate Gas ......................... 318
6.4 Evaluation of Contour Integrals ......................... 320
6.5 Diamagnetism of a Free Electron Gas; Oscillatory
Effect .................................................. 324
Chapter 7 Magnetic and Dielectric Materials ................. 329
7.1 Thermodynamics of Magnetic Materials in a Magnetic
Field ................................................... 329
7.2 Thermodynamics of Dielectric Materials in an Electric
Field ................................................... 333
7.3 Magnetic Effects in Materials ........................... 336
7.4 Adiabatic Cooling by Demagnetization .................... 340
Chapter 8 Lattice Dynamics .................................. 343
8.1 Periodic Functions of a Reciprocal Lattice .............. 343
8.2 Reciprocal Lattice ...................................... 343
8.3 Vibrational Modes of a Monatomic Lattice ................ 347
8.3.1 Linear Monatomic Chain ........................... 348
8.3.2 Density of States ................................ 358
8.4 Vibrational Modes of a Diatomic Linear Chain ............ 359
8.5 Vibrational Modes in a Three-Dimensional Crystal ........ 364
8.5.1 Properties of the Dynamical Matrix ............... 369
8.5.2 Cyclic Boundary for Three-Dimensional Cases ...... 373
8.5.2.1 Born-Von Karman Cyclic Condition ........ 373
8.6 Normal Vibration of a Three-Dimensional Crystal ....... 375
Chapter 9 Condensed Bodies .................................. 389
9.1 Application of Statistical Thermodynamics to Phonons .... 389
9.2 Free Energy of Condensed Bodies in the Harmonic
Approximation ........................................... 391
9.3 Condensed Bodies at Low Temperatures .................... 394
9.4 Condensed Bodies at High Temperatures ................... 397
9.5 Debye Temperature Approximation ......................... 398
9.6 Volume Coefficient of Expansion ......................... 403
9.7 Experimental Basis of Statistical Mechanics ............. 405
Chapter 10 Multiphase Systems ................................ 407
10.1 Clausius-Clapeyron Formula .............................. 407
10.2 Critical Point .......................................... 413
Chapter 11 Macroscopic Quantum Effects: Superfluid Liquid
Helium ....................................................... 421
11.1 Nature of the Lambda Transition ......................... 421
11.2 Properties of Liquid Helium ............................. 424
11.3 Landau Theory of Liquid He II ........................... 425
11.4 Superfluidity of Liquid Helium .......................... 430
Chapter 12 Nonideal Classical Gases .......................... 435
12.1 Pair Interactions Approximation ......................... 435
12.2 Van Der Waals Equation .................................. 441
12.3 Completely Ionized Gas .................................. 442
Chapter 13 Functional Integration in Statistical Physics ..... 449
13.1 Feynman Path Integrals .................................. 449
13.2 Least Action Principle .................................. 450
13.3 Representation of Transition Amplitude through
Functional Integration .................................. 456
13.3.1 Transition Amplitude in Hamiltonian Form ......... 460
13.3.2 Transition Amplitude in Feynman Form ............. 463
13.3.3 Example: A Free Particle ......................... 472
13.4 Transition Amplitudes Using Stationary Phase Method ..... 473
13.4.1 Motion in Potential Field ........................ 473
13.4.2 Harmonic Oscillator .............................. 476
13.5 Representation of Matrix Element of Physical Operator
through Functional Integral ............................. 479
13.6 Property of Path Integral Due to Events Occurring
in Succession ........................................... 481
13.7 Eigenvectors ............................................ 482
13.8 Transition Amplitude for Time-Independent Hamiltonian ... 483
13.9 Eigenvectors and Energy Spectrum ........................ 485
13.9.1 Harmonic Oscillator Solved via Transition
Amplitude ........................................ 485
13.9.2 Coordinate Representation of Transition
Amplitude of Forced Harmonic Oscillator .......... 488
13.9.3 Matrix Representation of Transition Amplitude
of Forced Harmonic Oscillator .................... 490
13.10 Schrodinger Equation ................................... 494
13.11 Green Function for Schrodinger Equation ................ 496
13.12 Functional Integration in Quantum Statistical
Mechanics .............................................. 497
13.13 Statistical Physics in Representation of Path
Integrals .............................................. 497
13.14 Partition Function of Forced Harmonic Oscillator ....... 503
13.15 Feynman Variational Method ............................. 504
13.15.1 Proof of Feynman Inequality .................... 506
13.15.2 Application of Feynman Inequality .............. 507
13.16 Feynman Polaron Energy ................................. 509
References ................................................... 519
Index ........................................................ 521
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