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Pathria P.K. — Statistical Mechanics

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Название: Statistical Mechanics

Автор: Pathria P.K.

Аннотация:

The first edition of this book was prepared over the years 1966-70 when the subject of phase transitions was undergoing a complete overhaul. The concepts of scaling and universality had just taken root but the renormalization group approach, which converted these concepts into a calculational tool, was still obscure. Not surprisingly, my text of that time could not do justice to these emerging developments. Over the intervening years I have felt increasingly conscious of this rather serious deficiency in the text; so when the time came to prepare a new edition, my major effort went towards correcting that deficiency.

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Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

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Издание: 2nd edition

Год издания: 1996

Количество страниц: 529

Добавлена в каталог: 01.07.2006

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Предметный указатель

$T^{3}$ -law of specific heats      177—178
$\epsilon$ -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 $T^{3/2}$ -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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