DeutschesFachbuch.de : Equilibrium Statistical Physics Phases of Matter and Phase Transitions Von M. Baus, Carlos F. Tejero

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Contents
Part I Basics
1 Mechanics 3
1.1 Classical Mechanics 3
1.2 Hamilton's Equations 4
1.3 External Parameters 5
1.4 Dynamical Functions 7
1.5 Quantum Mechanics 9
1.6 Self-adjoint Operators 10
1.7 Eigenvalue Equation 11
1.8 Schrödinger's Equation 13
1.8.1 Free Particle 14
1.8.2 Harmonic Oscillator 16
1.8.3 Particle in a Magnetic Field 16
1.9 System of Identical Particles 18
References 20
2 Thermodynamics 21
2.1 Fundamental Equation 21
2.2 Intensive Variables 23
2.3 Law of Entropy Increase 25
2.4 Thermodynamic Potentials 26
2.5 Equilibrium Conditions 28
2.6 Stability Conditions 29
2.7 Coexistence Conditions 32
2.8 Phase Diagrams 33
2.8.1 Gibbs Free Energy 33
2.8.2 Helmholtz Free Energy 37
2.8.3 van der Waals Loop 39
2.8.4 An Example of a Phase Diagram 41
References 43
3 Statistical Physics 45
3.1 Dynamical Functions and Fields 46
3.2 Liouville's Equation 48
3.3 Systems in Equilibrium 49
3.4 Density Operator 51
3.5 Ergodicity 53
3.6 Thermodynamic Limit 55
3.7 Symmetry Breaking 61
References 63
Part II Ideal Systems
4 Microcanonical Ensemble 67
4.1 Classical Microcanonical Ensemble 67
4.2 Classical Ideal Gas 69
4.3 Entropy and the Gibbs Paradox 71
4.4 Temperature and Thermal Equilibrium 75
4.5 Ideal Systems 77
4.6 Equipartition Theorem 78
4.7 Equation of State 79
4.8 Entropy and Irreversibility 81
4.9 Quantum Microcanonical Ensemble 83
4.10 Absolute Negative Temperatures 86
References 88
5 Canonical Ensemble 89
5.1 Classical Canonical Ensemble 89
5.2 Mean Values and Fluctuations 91
5.3 Helmholtz Free Energy 93
5.4 Classical Ideal Gas 94
5.5 Ideal Gas in an External Potential 95
5.6 Equipartition Theorem 97
5.7 Classical Theory of Radiation 99
5.8 Classical Theory of Solids 101
5.9 Quantum Canonical Ensemble 103
5.10 Ideal Quantum Systems 105
5.11 Maxwell-Boltzmann Statistics 106
5.12 Maxwell-Boltzmann's Ideal Gas 108
5.13 Brillouin's Paramagnetism 109
5.14 Photon Gas 111
5.15 Phonon Gas 114
References 119
6 Grand Canonical Ensemble 121
6.1 Classical Grand Canonical Ensemble 121
6.2 Mean Values and Fluctuations 125
6.3 Grand Potential 127
6.4 Classical Ideal Gas 128
6.5 Classical Ideal Gas in an External Potential 129
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Index
Aabsolute
- negative temperature, 86
- temperature, 22, 77
additive
- integrals of motion, 8
adsorption coefficient, 303
annihilation operator, 19
Asakura-Oosawa potential, 214
atomic description, 185
Avrami
- equation, 327
- exponent, 327
- theory, 327
Bbarometric formula, 96, 130
Becker-Döring theory, 316
bicritical point, 264, 265
bifurcation diagram, 248
- equation, 248
- point, 249
binary mixture, 210, 256
binodals, 39
body centered cubic lattice, 187
Bogoliubov method, 61
Bohr magneton, 17, 109
Bose-Einstein condensation, 146, 147
- critical specific volume, 151
- critical temperature, 145
- equation of state, 150
- specific heat, 147
- statistics, 140
bosons, 18, 106, 139
bounded operator, 13
Bravais lattice, 101, 186
Brillouin
- function, 109
- paramagnetism, 109
CCahn-Hilliard equation, 331
Carnahan-Starling equation of state, 199, 203
cell theory, 188, 190, 205, 234
central limit theorem, 349
chemical
- equilibrium, 33
- potential, 23, 123, 129
classical
canonical ensemble, 90
- grand canonical ensemble, 124, 125
- grand partition function, 123
- ideal gas, 69, 94, 128
- limit, 141
- microcanonical ensemble, 68, 179
- partition function, 90, 91
- scaling relation, 274
Clausius-Clapeyron equation, 36
close packing density, 188
closed system, 21
coexistence line, 35
colloidal suspensions, 211, 255
commutation rules, 9
complete set of commuting observables, 13
compressibility equation, 136, 137, 200
concave
- function, 338
- functional, 130, 133
conditional probability per unit of time, 181
conduction electrons, 153
conjugate momenta, 4 constant
- of motion, 8
- pressure heat capacity, 31
- pressure specific heat, 254
- volume heat capacity, 30
continuity equation, 47
continuous transitions, 37, 247
convex
- envelope, 39
- function, 338
- functional, 174
convexity condition, 252
convolution law, 76, 77, 85, 348
correlation
- length, 277
- matrix, 347
corresponding states law, 254
Coulomb potential, 58, 170
creation operator, 20
critical
classical exponents, 272
consolute point, 256
- dimension, 283
- endpoint, 263
- exponent, 254
- exponents, 270
- lines, 259
- non-classical exponents, 273, 288
- opalescence, 135, 276
- phenomena, 138, 269
- point, 37, 42, 201, 269
crystal phase, 186
Curie
- law, 111
- line, 261
- temperature, 62
current density
- dynamical function, 47
- field, 47
DD' Alembert equation, 99
Dawson function, 249
Debye
- frequency, 117
- screening parameter, 58, 216
- temperature, 118
- theory, 115
degree of polymerization, 224
degrees of freedom, 3 demixing phase transition, 211
density
- fluctuations, 126, 133, 135
- functional theory, 174
- of quantum states, 84
- operator, 52, 84, 138
- profile, 294
depletion mechanism, 213
Derjaguin-Landau-Verwey-Overbeek potential, 195, 215
detailed balance condition, 182
differential RG-equations, 284
direct correlation function, 172, 201, 276
discontinuous transitions, 248, 291
disordered phase of a mixture, 209
dispersion relation, 100, 115, 117
displacement
- tensor, 102
- vector, 102, 186
distinguishable particles, 19, 106
dividing surface, 303
Dulong-Petit law, 103, 115
dynamical function, 7
Eeffective
- hamiltonian, 212
- one-particle potential, 172
- potential energy, 212
Ehrenfest thermodynamic classification, 251
eigenvalue, 11
eigenvectors, 11
Einstein
- classical model, 73, 98, 193
- quantum model, 115
- temperature, 115
elastic
- constants, 309
- deformations, 309
energy
equation, 77, 92, 125
- fluctuation, 92, 126, 129
- of mixing, 211
- representation, 25
- surface, 68
entropy
- additivity , 77
- of mixing, 211
- production, 25
- quantum, 85
- representation, 25
- statistical, 69, 80
- thermal variable, 22
- thermodynamic, 69, 81
equation of state, 79, 80, 92, 127
equilibrium system, 21
equipartition theorem, 78, 97, 98, 101, 129, 193
ergodic theory, 54
Euler gamma function, 70
excluded
- region, 214
- volume interaction, 189
- volume of two spherocylinders, 220
external
- parameters, 5, 79
- potential, 4, 95, 171
extremum principle, 28
Fface centered cubic lattice, 188
Fermi
- energy, 153
function, 153
- temperature, 156
Fermi-Dirac
- statistics, 140, 153
fermions, 18, 106, 139 first
- law of thermodynamics, 22
- order transition, 151, 251, 261
- postulate of classical statistical physics, 48
- postulate of quantum statistical physics, 52
fixed points, 281, 286
Flory exponent, 225, 278, 282, 287
Flory-Huggins
- mixing parameter, 228
- theory, 226, 259 fluid phase, 196, 208
fluid-solid transition, 234 forbidden symmetries, 355
fork bifurcation, 249
Fourier transform, 348
Frank planar model, 310
- Frank-Oseen expression, 309
free
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