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Авторизация |
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Kubo R. — Statistical Mechanics: An Advanced Course with Problems and Solutions |
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Предметный указатель |
Entropy, probability and 19 51
Entropy, statistical definition of 8 18
Entropy, thermodynamic definition of 8 18
Equation of motion, canonical 2
Equation of state 35 193 257 288
Equation of state of Fermi gas 253 268
Equation of state, Van der Waals 322
Equilibrium condition for two phases 134 153
Equilibrium constant of chemical reaction 202 211 222
Equilibrium, thermal, state 5 15
Equipartition, law of, of energy 112 253 265
Ergodic hypothesis 87
Ergodic surface 2 4 87
Ergodic theorem 6 86 215
Error integral 406
Euler — Maclaurin summation formula 193
Eulerian angles 201
Euler’s summation formula 259 298
Euler’s theorem 113
Exchange integral 303 313
exchange interaction 303 308 313 322
Expansion coefficient, cubic 164
Expectation value, quantum mechanical 3
Fermi momentum 258 289
Fermi particle 29 186 228 257
Fermi potential (level, energy) 228 233 240 243 251—256 260 263 265 273 276 287
Fermi surface 372
Fermi — (Dirac) statistics 28 53 60 62 94 182 228 245
Fermi-Distribution 29 229 247 252 262 265 267 373
Fermi-distribution for holes 273
Fermi-gas, compressibility of 253 268
Fermi-gas, degenerate 231 232 265 267
Fermi-gas, density matrix for 259 295
Fermi-gas, equation of state of 253 268
Fermi-gas, Helmholtz free energy of 229
Fermi-gas, ideal 228 259 266 281 295
Fermi-gas, internal energy of 240
Fermi-gas, relativistic 257—259 288—291
Fermi-gas, specific heat of 241 251—253 262 267
Fermi-gas, thermodynamic functions of 30
Fermion 29 186 228 257
Ferromagnetic crystal 313
Ferromagnetic substance 160 321
ferromagnetism 302 303 307 322 329 332
Ferromagnetism, Heisenberg 332
Flory, P.J. 159 387
Flory’s approximation 327
Fluctuating force 378
Fluctuation 19 361
Fluctuation dissipation theorem 374 416
Fluctuation in energy 41 44 130
Fluctuation in number of solute molecules 375
Fluctuation in particle number 398
Fluctuation in total magnetic moment 62
Fluctuation of coordinates 395
Fluctuation of thermodynamical variables 375
Fluctuation process 374
Fluctuation, probability distribution of 366
Fluctuation, thermal 417
Fluctuation, thermodynamic theory of 361
Folding property 103
Fowler 104
Fowler and Guggenheim 119
Fowler plot 283 341 355 357
Fowler — Darwin method see “Saddle point method”
Free energy, Gibb’s 47 82 219
Free energy, Helmholtz 27 45 47 49 82
Frenkel, lattice defects of, type 90
Friction constant 376
Fugacity 192
g-factor, Lande’s 150
Gauss theorem 34
Gauss transformation 296
Gaussian distribution 21 57 74 375
Generalized coordinates 2 132
Generalized entropy 31
Generalized force 26
Generating function 72 109
Gibbs 4
Gibbs free energy 47 82 219
Gibbs paradox 188
Gibbs — Duhem relation 386
grand canonical ensemble see “Distribution”
Gravitational constant 141
Green’s function 397
Groot, S.R. de 374
Grueneisen’s assumption 137 164
H-Theorem 31 51 215
Haar, D. ter 174
Haas, de, van Alphen effect 259 300
Hamiltonian 2 3
Hamiltonian for harmonic oscillators 70 280
Hamiltonian for rotational motion 115
Hamiltonian for system of charged particles 138
Hamiltonian in rotating coordinate system 142
Hamiltonian of a rotator 200
Hamiltonian of electron in magnetic field 138 174
Hamiltonian of spins in electric field 313
Hamiltonian of system of interacting particles 171
harmonic oscillator 57 59 71 78 83 120 123 134 138 251 255 265 279 380
Harmonic oscillator, energy levels of 36
Harmonic oscillator, Hamiltonian 70 280
Harmonic oscillator, number of states of 59 61 78
Harmonic oscillator, partition function for a single 123
Harmonic oscillator, state density of class 137 168
Harmonic oscillators, system of, average energy of 38
Harmonic oscillators, system of, density matrix of 139
Harmonic oscillators, system of, energy of 38
Harmonic oscillators, system of, entropy of 37 81
Harmonic oscillators, system of, Helmholtz free energy of 81 117
Harmonic oscillators, system of, partition function of 59 80 116
Harmonic oscillators, system of, specific heat of 218
Hartree — Fock approximation 303
Heat bath 21 23 62 132
heat capacity see “Specific heat”
Heat capacity of crystal 136
Heat capacity of solids 136
Heat conductivity 362 369 370 374 378 379 389 403 410 413 415
Heat flux 370 374
Heat radiation 123 132 136 146
Heat source 84
Heisenberg ferromagnetism 322
Heisenberg model 313
Helmholtz free energy 27 45 47 49
Hemmer, P. 322
Hermite polynomial 138
Heteronuclear molecules 185
Hildebrand 337
hole 91 234 243 273
Homonuclear molecule 185
Hooke’s law 78
Hopf 87
Hove, L. van 216
Hydrogen 223 (see also “Para-hydrogen” “Ortho-hydrogen”)
Ideal gas 4 35 46 57 59—61 82 83 103 131 137
Ideal gas, chemical potential of 48
Ideal gas, entropy of 35 48
Ideal gas, Gibbs’ free energy of 47
Ideal gas, Helmholtz free energy of 27 45 47
Ideal gas, mixtures of ideal gases 188
Ideal mixture, entropy of 305
Ideal quantum gas 51 (see also “Bose-gas” “Fermi-gas”)
Ideal quantum gas, (grand) partition function of 54
Ideal quantum gas, entropy of 51
Ideal quantum gas, Helmholtz free energy of 51
Imperfect crystal 90 61
Imperfect crystal, entropy of 91
Imperfection of Schottky type 61
Impurity 377
Impurity atom 353
| Impurity semiconductor 236
Indistinguishability of identical particles 9 82 182
Inertia see “Moment of inertia”
Integral kernel 397
Internal partition function 184 206
Interstitial atoms 90
Interstitial sites 61
Intrinsic semiconductor 236 243 286
Inversion symmetry 338
Ionic charge 324
Ionic interactions 310
Ionic solution 310 318
Irreducible cluster integral 193 205 227
Irreducible diagram 227
Irreversible process 361 373 416 417
Ising model 303 324 326
Ising spin 303 321 327 328
Ising spin system 328
Ising spin system, energy of 326 349
Ising spin system, free energy of 326 349
Ising spin system, partition function of 355
Ising spin system, specific heat of 322 329
Isotherm, Langmuir’s 93
Isothermal compressibility 165 377 399
Jacobian 383
Joule — Thomson coefficient 204 223
Joule — Thomson effect 222
Kac, M. 322
Keesom force 170
Kernal, integral 397
Khinchin 87 106 174
Kinetic coefficients 374 (see also “Transport-coefficients”)
Kinetic theory of gases 5 51 60 361
Kirkwood’s approximation 321 328
Knudsen (gas) region 388
Koopman 87
Kronecker’s delta 410
Kubo 402 416
Kubo’s formula 415
Lagrange’s undetermined multipliers 20 86 95
Landau 299
Landau level 298
Langevin Debije formula 266 287
Langevin equation 378
Langevin’s function 126 158
Langmuir’s isotherm 93
Laplace transform 172
Laplace transform, inverse 104 259
Lattice 161 307 349
Lattice defects of Frenkel type 90
Lattice imperfection of Schottki type 61
Lattice model 337
Lattice points 90
Lattice site 61 306
Lattice vibration 160 265 302
Lattice, crystal 160
Lattice, regular (ordered, superlattice) 307 377
Lattice, sub 307 316 322
Legendre transformation 25 28 85 107 127
Lennard-Jones potential 189
Linearization of Boltzmann’s equation 366
Liouville equation 412
Liouville theorem 87
liquid helium 238 239 309
Local equilibrium 410
Local flow velocity 380
Local number density 379
Local temperature 380
London 250
Long range 309
Long range order 321 323 327 347 355
Lorentz 245
Lorentz force 255
Lorentz’s flow 404
Lorentz’s number 404
Loschmidt 215
Macroscopic state 7
magnetic moment 133 263 304
Magnetic moment of spin 252 276 303
magnetic quantum number 133 149
Magnetic quantum state 150
magnetic susceptibility 133 138 256 257 259 299 325 346
magnetization 133 149 171 303 309 322 332
Magnetization waves 160
Magnetization, saturation 305 332
Magnetization, spontaneous 304 307 325 331 343
Many body problem 303
Masers 148
Mass action, law of 247 357
Maximum term method 106
Maxwell 51
Maxwell distribution 5 31
Maxwell relation 381 382
Maxwell’s Demon 13
Maxwell’s equation 369
Mayer, J.E. and M.G. 193 227
Mayer, J.E. f(r) function 190
Mazur, P. 374
Mean free (flight) time 362 366 367 369 380 413
Mean free path 366 370 379 389 393
Mean number of collisions 368
Mean square displacement 378
microcanonical ensemble see “Distribution”
Microscopic state 1
Mie — Gruneisen’s equation 137
Mobility 402
Molecular chaos 363
Molecular crystal 338
Molecular field approximation 302 306 313 314 321—328 332 356 357
Molecular field constant 303 314
Molecular interaction 189
Moment of inertia (tensor) 185 200 202 219 224 376
Moment, magnetic 133 263 304
Moment, magnetic, of spin 252 276 303
Monatomic molecules 184
Mot-screening constant 353
Mulholland’s formula 194
Nearest neighbor interaction 323
Nearest neighbor, number of 304 327 328 335
Nearly ideal gas, thermodynamic properties of 205 226
Neel temperature 309 325 344
Neumann 87
Neutron 29 85
Neutron diffraction 307 309
Non-degeneracy see “Degeneracy”
Non-degenerate see “Degenerate”
Normal distribution 384
Normal modes 116 120 136 160 163 251 302
Normal system 10 147
Normal system, entropy of 11
Normal system, not 39 99
Normal vibrations 116 120 136 160 163 251 302
Nuclear spin 184 186 201 208 219 221
Nuclear spin, degeneracy of, states 184 187 221
Number density 326 341 365
Number density, local 379
Number of neighboring spins 304 327 328 335
Nyquist’s equation 416
Occupation number 29
Occupation number, average 29 228
Onsager 322
Onsager’s reciprocity relations 373 404
Order parameter 307
Order-disorder transition 307 309 328 335
Order-disorder transition of alloys 307
Ordering, perfect 308
Orientational distribution function 379
Ortho-deuterium 187
Ortho-hydrogen 187 201 208 210
Orthogonal transformation 177
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