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| Pathria P.K. — Statistical Mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
 -law of specific heats 177—178
 -expansion 436—439
Adiabatic processes 17 21 28 153 259
Adiabats of a Bose gas 167
Adiabats of a Fermi gas 229
Adiabats of black-body radiation 172
Adsorption 103
Anharmonic oscillators 86 87
Antiferromagnetism 316 320 361
Autocorrelation functions 466—467 474—479 481—484 491—492
Barometric formula 153
beta function 499
Beth — Uhlenbeck formalism 249—253 260
Bethe approximation to the Ising lattice 328—334 362 369 383 386—387 408 410
Binary alloys 321 361—362
Binary collision method 258—259 276 293 303 304
Binding energy of a Thomas — Fermi atom 226—227 231
Black-body radiation 168—172 190—191
Bloch's  -law 360
Block-spin transformation 415
Bogoliubov transformation 274—275
Bohr — van Leeuwen theorem 88 208
Boltzmann factor 2 61—62 87 135 153
Boltzmannian systems, classical 16 30 56 129—132 135 137 232—245
Boltzmannian systems, quantum-mechanical 258 260
Bose gas, imperfect 270—277 299—300
Bose liquids, energy spectrum of 277—280 300
Bose — Einstein condensation 160—168 187 188—190 193 400—403
Bose — Einstein condensation, with interactions 270—273 278 299—300
Bose — Einstein functions 159 506—508
Bose — Einstein statistics 5 6 119 127—137 148—149
Bose — Einstein systems 120—124 127—137 157—194 249—260 490
Bose — Einstein systems, multi-dimensional 190 192 398—404
Bose — Einstein systems, nonuniform 283—285
boundary conditions 449 495—497
Bragg — Williams approximation to the Ising lattice 321—327 332 333 360—362 383 386—387 410
Brillouin function 75—76
Broken symmetry 324 365
Brownian motion 452 459—469 470—474 490—492
Brownian motion of a suspended mirror 472—474 490
Brownian motion, observation of 462 480 490
Canonical distribution 34 45 51 53 55
canonical ensemble 34 43—56 60—63 83 85 109—110 131—133
Canonical transformations 40 64
Chandrasekhar limit 222
chemical potential 14 54 90—92 see
Chemical potential of a Bose gas 272—273
Chemical potential of a classical gas 24—25
Chemical potential of a Fermi gas 200 204—205 214 227—230
Chemical potential of a Fermi liquid 297 302
Chemical potential of a gas of phonons 193
Chemical potential of a gas of photons 193
Circulation, quantized 280—288 300—301 303
Classical limit 26 122 135 140 160 193 196—197
Classical systems 15—25 30—34 56—60
Classical systems in the canonical ensemble 56—60 132
Classical systems in the grand canonical ensemble 132—133
Classical systems in the microcanonical ensemble 131
Classical systems, interacting 63—6 232—245
Cluster expansions, classical 232—239
Cluster expansions, general 245—249
Cluster expansions, quantum-mechanical 254—258
Cluster functions 256—257 260
Cluster integrals 235—236 239 246 248 257 260
Cluster integrals, irreducible 239 248 261 359
Complexions see "Microstates"
Compressibility, adiabatic 189 228 412
Compressibility, isothermal 101 189 228 412 454 458
Condensation 306—310 see
Condensation of a van der Waals gas 310—314
Condensation, scaling hypothesis for 363
Condensation, Yang — Lee theory of 310
Conductivity, electrical 209 212 484
Conductivity, thermal 209 212
Configuration integral 233—237 245—246 254—255
Configurational distribution functions 456—458
Conformal transformation 440—441
Cooperative phenomena see "Phase transitions"
Coordination number 318 365
Correlation function 349—351 354—355 364 418
Correlation function in the mean-field approximation 351—353 358 363
Correlation function in the scaled form 354 446
Correlation function of a Bose gas 402—403 411
Correlation function of a fluid 457—459
Correlation function of an n-vector model 373—375
Correlation function of the Ising model 371 387—388 410
Correlation function of the spherical model 395—397 411
Correlation function of the X-Y model 405
correlation length 353 355 364 406 414 417
Correlation length in the mean-field approximation 352—353 359
Correlation length of a Bose gas 403 411
Correlation length of an n-vector model 374—376 409
Correlation length of the Ising model 371—372 387—388 408 409
Correlation length of the spherical model 396—397 411
Correlation length of the X-Y model 404—405
Correlations, spatial 123—124 452 456—459
Correlations, spin-spin 289 331
Correlations, statistical 123—124 137 490 494
Corresponding states, law of 312
Covariance matrix 489 494
Critical behavior of a Bose gas 161—165 400—402 412—413
Critical behavior of a fluid 363
Critical behavior of a magnetic system 342—343 346—347 351—353 363
Critical behavior of a van der Waals gas 311—314 359
Critical behavior of the Ising model 324—326 329—333 370—372 383 385—388 410 432 434—436 450
Critical behavior of the spherical model 392—395 411 433
Critical behavior of the X-Y model 404—405
Critical curve 435 437 451
Critical dimension, lower 404 441 445 448
Critical dimension, upper 357 398 441 448
Critical exponents 334—338 353—356 362 363 364 451
Critical exponents of a Bose gas 401—404
Critical exponents of an n-vector model 375 407 437 438—439 451
Critical exponents of polymers 407
Critical exponents of the Ising model 370 372 388 407 432 434
Critical exponents of the spherical model 395—397 407 411—412 433
Critical exponents, experimental values of 336
Critical exponents, hyperscaling relation among 355—357 406
Critical exponents, mean-field values of 335 342—343 353—355 407 430—431
Critical exponents, scaling relations among 346—347 355—356 364 406
Critical exponents, theoretical values of 406—407
Critical exponents, thermodynamic inequalities for 338—341 355—356 362
Critical opalescence 101 452 459
Critical surface 427—429 451
Critical trajectories 428
Critical velocity of superflow 180 187—188 194 285—258 301
Crossover phenomena 440
Curie temperature 324 329—330 360
Curie — Weiss law 326 343 353 360
Curie's law 73 75 203 205 208
Darwin — Fowler method 47—52
Debye function 176 191
Debye temperature 176—178 191 211
Debye's theory of specific heats 175—178 191—192
Decimation transformation 415—418 418—426 426—431 449
Degeneracy criterion 122—123 140 157 193 see
Delta function 501—503 505
Density fluctuations 100—101 455—456 458 490
Density fluctuations, in the critical region 459
Density function in phase space 4 31—34
Density matrix 6 104—110 124—125 126
Density matrix of a free particle 111—113 255
Density matrix of a linear harmonic oscillator 113—115
Density matrix of a system of free particles 119—124
Density matrix of a system of interacting particles 254—256
Density matrix of an electron 111 124
Density of states 20 56 59—60 230 250—252
Density of states for a free particle 37 230 495—497
Density of states for a system of harmonic oscillators 68 70
Detailed balancing 106
| Diamagnetism, Landau 202 206—209
diatomic molecules 87—88 103 142—150 154—156
Dietrici equation of state 359
Diffusion coefficient 463 465 471 481—483
Diffusion equation 463 471
Diffusion, Brownian motion in terms of 463—464
Dipole-dipole interaction 88
Dirac delta function 501—503 505
Dissipative phenomena 452 464 481—484
Distribution functions, configurational 456—458
Doppler broadening 153
Duality transformation 381—382
Dulong — Petit law 175
Edge effects 496
effective mass 187 192 208 210 231 296—297 299 302 304
Effusion 139 154
Effusion of electrons from metals 213—216 216—218
Effusion of photons from a radiation cavity 171
Einstein function 174
Einstein — Smoluchowski theory of the Brownian motion 459—462
Einstein's relations 452 465—466
Electron gas in metals 5—6 209—218
Electrons in a magnetic field 111 206—209
Elementary excitations in a Bose liquid 277—280 280—285 285—288 300—301
Elementary excitations in a Fermi liquid 293—299 302
Elementary excitations in an imperfect Bose gas 273—277 300
Elementary excitations in liquid helium II 182—188 192 279—280 285 287
Energy cells 127—130
Energy fluctuations 60—3 85 101—102 455—456
Ensemble average 31 35 105 107
Ensemble of Brownian particles 463 470—472 482
Ensemble theory 3—4 6 30—36 43—55 60—63 90—95 100—102 104—110
Enthalpy 15
entropy 12—13 20 22—4 27 36 54—55 71 95 166 196
Entropy in nonequilibrium states 453—455 485—487
Entropy of an Ising ferromagnet 326 361 362 410
Entropy of mixing 22—24
Entropy, statistical interpretation of 13 54—55 102 108
Equation of state see also "van der Waals equation of state"
Equation of state of a Bose gas 159—160 253 272
Equation of state of a Fermi gas 197 253
Equation of state of a lattice gas 360 409 410
Equation of state of classical systems 16 21 65—66 238—245 247—249 359
Equation of state of quantum-mechanical systems 247—249 258 299 301
Equation of state, reduced 312
Equilibrium constant 85 154 331
Equilibrium, approach to 11—12 13—14 452 469—472 485
Equilibrium, deviations from 453—456 489—490
Equilibrium, persistence of 468
Equipartition theorem 63—65 86 151 153 465 468 472 473 479
Equipartition theorem, failure of 65 143 145—146 149 151 165 174—175 200—201 209
Ergodic hypothesis 41
exchange interaction 315—316
Exclusion principle 5 29 118 128 198 231 267 268 493
Extensive variables 9—10 22 24 28
Factorial function 497—501
Fermi energy 198 200 202 205 210 214—215 219 229—230
Fermi gas, imperfect 289—293 297—299 301—302
Fermi liquids, energy spectrum of 293—299 302
Fermi momentum 198 219 220 224 231 294 302
Fermi oscillators 87
Fermi temperature 200 210 219 227 229
Fermi velocity 229 295
Fermi — Dirac functions 195 508—510
Fermi — Dirac statistics 5 6 118—119 127—137 148—149
Fermi — Dirac systems 120—124 127—137 195—231 249—260 490
Fermi — Dirac systems, n-dimensional 229
ferromagnetism 314—316 320 323—326 329—330 see
Feynman's circulation theorem 281
Feynman's theory of a Bose liquid 278—282 285 300
Fick's law of diffusion 463
Field-theoretic approach 262—270
Finite-size effects 18—19 190 397 411 412 413 441—449 495—497
Finite-size scaling 441—449
Fixed point 406 427—428 432—433 435 450
Fixed point, Gaussian 436—437
Fixed point, non-Gaussian 436—437
Fluctuation-dissipation theorem 350 354 356 409 447 452 481—484 487
Fluctuations 452—494 see "Phase
Fluctuations in a multiphase system 364
Fluctuations in an (L,R)-circuit 480—481
Fluctuations in an electrical resistor 483—484
Fluctuations in the canonical ensemble 51—2 60—63 85
Fluctuations in the grand canonical ensemble 100—102 103
Fluctuations of occupation numbers 7 136—137 155
Fluctuations thermodynamic 453—456 489—490
Fluctuations, critical 101 459 492
Fluctuations, frequency spectrum of 474—481
Flux quantization in superconductors 303
Fokker — Planck equation 469—472 491
Fourier analysis of fluctuations 474—481 491—492
Fowler plot 218
Free volume 84—85
Fugacity 94 98—99 110 213 238—239 247—248 see
Fugacity of a Bose gas 161—162 273 299
Fugacity of a Fermi gas 200 227 292 301
Fugacity of a gas of phonons 193
Fugacity of a gas of photons 193
Fugacity of a lattice gas 319—320 409
Fugacity of a two-phase system 98—99
Gamma function 497—501
Gaussian model 389
Gibbs free energy 15 24—25 54
Gibbs paradox 22—25 25—26
Ginzburg criterion 357
Goldstone modes 376
grand canonical ensemble 90—95 100—103 110
Grand partition function 94—95 110
Grand partition function of a lattice gas 319
Grand partition function of a multiphase system 308—310
Grand partition function of an ideal gas 133—134 158 195
Grand partition function of an imperfect gas 238 245 299 301
Ground-state properties of a Bose gas 270—272 273—277 300
Ground-state properties of a Fermi gas 197—199 202—203 205 209 220—221 226—227 230 231 292—293 297—299 301—302
H-Theorem 3
Hard sphere gas 1 27 86 243—245 252—253 303
Harmonic approximation 173
Harmonic oscillators 27 37—38 41 66—71 86 97—98 168—169 173—178
Heisenberg model 316 360
Helicity modulus 365
Helmholtz free energy 15 25 53 95
Hyperscaling relation 355—357 430—431
Ideal gas of bosons 158—168 398—404 412—413
Ideal gas of fermions 195—209
Ideal gas, classical 15—25 36—37 57—60 62—63 65 96—97
Ideal gas, quantum-mechanical 115—124 127—139
Indistinguishability of particles 5 25—26 96 117—119 127—129
Indistinguishability of photons 5 169
Inertial density of excitations 179—182 186 192
Integrating factor for heat 94
Intensive variables 10 28
Internal molecular field 323 328 360 see
Internal motions of molecules 140—152 154—155 190
Irrelevant variables 429 434 437 451
Irrelevant variables, dangerously 430—431 437
Irreversible phenomena 3 452 459 463—465 469 484—489 493
Ising model 316 319 321—334 360 362
Ising model in one dimension 366—372 407—409 418—421 432
Ising model in three dimensions 405—407
Ising model in two dimensions 377—388 410 423—426 433—436
Isothermal processes 21 see
Isotherms of a Bose gas 166
Isotherms of a multiphase system 307—308 310
Isotherms of a van der Waals gas 311
Joule — Thomson coefficient 260
Kinetic coefficients 484
Kinetic pressure 1—2 138—139 192
Kirkwood approximation 362
Kramers' q-potential 93 103 see
Kubo's theorem 484 487
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