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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

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 1996

Количество страниц: 529

Добавлена в каталог: 01.07.2006

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Предметный указатель

Lagrange multipliers, method of      47 89 129
Lambda-transition in liquid He4      165—166 187
Landau diamagnetism      202 206—209
Landau's condition for superflow      282 see
Landau's spectrum for elementary excitations in a Bose liquid      182—184 278
Landau's theory of a Fermi liquid      293—299
Landau's theory of phase transitions      341—344 363
Langevin function      72—73 207
Langevin's theory of the Brownian motion      464—469 490—491
Langevin's theory of the Brownian motion, as applied to a resistor      483
Langmuir equation      103
Lattice gas      319—321 360 409 410
Law of mass action      85 331
Length transformation      406 414—418 418—426 426—431
Lennard — Jones potential      240 242 259
Light scattering by a fluid      348—349 353 458—459
Liouville's theorem, classical      32—34
Liouville's theorem, quantum-mechanical      106
Liquid $He^{3}$ , specific heat of      178 304
Liquid $He^{4}$       see also "Superfluid density"
Liquid $He^{4}$ , elementary excitations in      182—188 192
Liquid $He^{4}$ , normal fraction in      181—182 186—187
Liquid $He^{4}$ , specific heat of      165—166 178 186
Long-range interactions      334 337 365 398 411 440
Long-range order      314 321 459 see
Long-range order in a binary alloy      361—362
Long-range order in a Bose gas      403
Long-range order in a square lattice      386—387
Long-range order in the Bethe approximation      329—3230
Long-range order in the Heisenberg model      360
Long-range order in the spherical model      397
Long-range order in the Weiss ferromagnet      323—325
Lorenz number      209—210 212
Macrostates      9—10 34 43
Magnetic systems, thermodynamics of      71—83 88 103 see "Paramagnetism"
Marginal variables      429
Markovian processes      493
Mass motion      179—182 186 187—188 192
Mass motion, nonuniform      280—288 300—301
Mass-radius relationship for white dwarfs      221—223
Master equation      470 493
Maxwell — Boltzmann statistics      2—3 5 129 131 132—133 135 137 153 see "Classical
Maxwell's construction      307—308 311 342 344 364
Mayer's function      86 233—234 243 256
Mayer's theory of cluster expansions      232—240 248—249
Mean field theories      321—327 328—334 360—362 365
Mean field theories, limitations of      356—359
Mean values, method of      47—52 93
Meissner effect in superconductors      303
Memory functions      see "Autocorrelation functions"
Mermin — Wagner theorem      404
microcanonical ensemble      34—36 55 60—61 63 107—109 127—131
Microstates      10—15 17—20 37 107 116—117 127—130
Microstates, "correct" enumeration of      25—26
Microstates, of a binary alloy      361
Microstates, of an Ising ferromagnet      326 360 408
Migdal — Kadanoff transformation      450
Mobility      464—465 471—472 481
Monte-Carlo methods      406
Most probable distribution      46—47 92 129—130 408
Most probable values, method of      46—47 129
Mulholland's formula      145
Neel temperature      361
Negative temperatures      80—83 88
Nernst heat theorem      see "Third law of thermodynamics"
Nernst relation      465—466
Noise      452
Noise in an (L,R)-circuit      480—481
Noise, white      476—477 479—481 484 493
Nonequilibrium properties      481 484—489 see
Normal modes of a liquid      178
Normal modes of a solid      173—176 191—192
Nyquist theorem      481
Occupation numbers      25—26 116—119 127—137 169 197—199
Onsager relations      484—489
Order parameter      341—342 346 364 386—387 446
Ortho- and para-components      149—150
Pade approximants      405
Pair correlation function      457—459 490 492 494 see "Correlations"
Pair distribution function      66 86 123—124 457—459 492 494
Paramagnetism      71—77 201—205 230 302 368—369 409—410
Particle-number representation      263—8 303
Partition function      53 55—56 62 109 119—123 125 131—132
Partition function of a Bose gas      272
Partition function of a classical ideal gas      57—59 84 85 96 132
Partition function of a Fermi gas      203—204
Partition function of a system of free particles      112 119—123 131—133 140
Partition function of a system of harmonic oscillators      67 68 70 97 114
Partition function of a system of magnetic dipoles      72 75 77 82 88
Partition function of a two-phase system      306—309
Partition function of an interacting system      233—238 245 249 254—258 272
Partition function of an n-vector model      372—373 411
Partition function of the Ising model      317—318 367—368 378—383 408—410 418—420 423—425
Partition function of the lattice gas      319
Partition function of the spherical model      389—391 421—422 449
Pauli paramagnetism      202—205 230
Pauli's exclusion principle      see "Exclusion principle"
Perturbation theory      274 290
Phase separation in binary mixtures      362
Phase space      3 30—34 36—40 41 57 122
Phase transitions      305—451 see
Phase transitions and correlations      330—331 348—353 406 414 452 458—459
Phase transitions and fluctuations      101 348—353 356—359 398 408 458—459
Phase transitions in finite-sized systems      441—449
Phase transitions, a dynamical model of      314—319
Phase transitions, first-order      363 448
Phase transitions, interfacial      440
Phase transitions, Landau's theory of      341—344 363
Phase transitions, second-order      341 363 448
Phonons      172—178
Phonons in a Bose fluid      277 280
Phonons in liquid helium II      178 181—182 183
Phonons in mass motion      179—181 186
Phonons, effective mass of      192
Photoelectric emission from metals      212 216—218
photons      5 39—40 168—172 190—191
Poisson equation      224
Polyatomic molecules      150—152 155 191
Postulate of equal a priori probabilities      10 34 107—109
Postulate of random a priori phases      108—109
Power spectrum of a stationary variable      475—481 491—492
Predictability of a variable      474 476 478
Probability density operator      254—256 see
Probability distribution for Brownian particles      459—462 470—473 491
Probability distribution for thermodynamic fluctuations      453—456 489—490
Pseudopotential approach      276 277 293 303 304
Q-potential      93—95 102 see
q-potential of a two-phase system      309—310
q-potential of an ideal gas      133—134
Quantized circulation in a Bose fluid      188 280—288 300—301 303
Quantized fields, method of      262—277 289—293 299 300
Quantized flux      303
Quantum statistics      5—6 26 104—124 127—139 see "Fermi
Quasi-chemical approximation to the Ising lattice      328 331 408 see
Quasi-particles      see "Elementary excitations"

Random mixing approximation      327 332 360 361 362 365 see
Random walk problem      459—461 471
Randomness of phases      108—109 475
Ratio method      405
Rayleigh — Jeans law      170
Relativistic gas      27 39—40 41 85 153
Relativistic gas of bosons      193 404 412—413
Relativistic gas of electrons      220—223 230
Relativistic gas of fermions      231
Relaxation time      464 470 480 482 492 493
Relevant variables      428 434
Renormalization group approach      406 414—441
Renormalization group approach to the Ising model      418—421 423—426 432 433—436 449
Renormalization group approach to the spherical model      421—423 432—433 449
Renormalization group approach, general formulation of      426—431
Renormalization group operator      426 451
Renormalization group operator, linearized      427 450
Response time      480
Richardson effect      213—215 230
Riemann zeta function      506—507
Rigid rotator      40 144—150 151 155
Rotons in a Bose fluid      278—280
Rotons in liquid helium II      183—188 192 193—194
Sackur — Tetrode equation      24
Saddle-point method      47—52 83 390
Scalar models      365 366—372 375—376 404
Scaling fields      428 434
Scaling hypothesis      344—348 354 363
Scaling relations      346—347 355—356 364 417—418 430—431
Scaling theory      415—418 429—431
Scattering of e.m. waves by a fluid      348—349 353 458—459
Schottky effect      215—216
Schottky specific heat      79
Second quantization      262—270 see
Short-range order      327 331 332 362
Singularities in the thermodynamic functions      164—166 189 190 272—273 299 300 see "Specific-heat
Smoluchowski equation      460—461
Solid-vapor equilibrium      98—100 103
Sommerfeld's lemma      199—200 292 302 510 512
Sommerfeld's theory of metals      210
Sound waves      172—178 see
Sound waves, inertial density of      179—182
Specific heat      15 54 61 454 455 456
Specific heat of a Bose gas      160 163—165 167 188—189 399—402 412
Specific heat of a classical gas      21
Specific heat of a Fermi gas      197 200—201 210—211 228—230
Specific heat of a system of harmonic oscillators      67 69 87 174—178 191
Specific heat of an imperfect gas      299 300 301
Specific heat of an Ising lattice      324—325 332—333 369—370 383—386
Specific heat of an n-vector model      375—376
Specific heat of black-body radiation      172
Specific heat of diatomic gases      143—150
Specific heat of liquid helium II      165 178
Specific heat of magnetic materials      77 79 83 88
Specific heat of polyatomic gases      151
Specific heat of solids      174—178 191 211
Specific heat of the spherical model      392—395
Specific heat of the X-Y model      405
Specific-heat singularity      164—165 189—190 299 325 333 385—386 394—395 401—402 405
Spectral analysis of fluctuations      474—481 491—492
Spherical constraint      389 390 392—393 411 421 422 449
Spherical field      391
Spherical field, reduced      392—397
Spherical model      376 389—398 410—412 421—423 432—433 449
Spin and statistics      6 119 148—150 260 269
Spontaneous magnetization      314—315 318 346 365 see
Spontaneous magnetization in the Ising model      323—324 329—330 386—387 410
Spontaneous magnetization in the spherical model      394 397 411
Square-well potential      260
Stationary ensembles      4 32 33 35 106 466 482
Stationary variables, Fourier analysis of      474—481 491—492
Statistical potential      124 252
Steepest descent, method of      47—52 83 390
Stefan — Boltzmann law      171
Stirling's formula      499—501
Stokes law      493
Structure factor of a liquid      278—280 303
Superfluid density near critical point      364
Superfluid in mass motion      187—188 280—285 286—287
Superfluid transition in liquid $He^{4}$       165 187 364
Superfluidity      see also "Critical velocity of superflow"
Superfluidity, breakdown of      187—188 285—288
Superfluidity, Landau's criterion for      187—188 287—288
Surface effects      495—497
Surface tension near critical point      364 388
Susceptibility, magnetic      73 75 346 350—351 353 355 356—357 see
Susceptibility, magnetic of a Fermi gas      203 205 208—209 230 302
Susceptibility, magnetic of an n-vector model      410
Susceptibility, magnetic of the Ising model      326 343 362 369 388 410
Susceptibility, magnetic of the spherical model      392—396 411
Sutherland potential      259
Symmetry properties of the wave functions      7 118 120 148 251 260 263—265 278 280—281
Thermal expansion, coefficient of      192 259
Thermal wavelength, mean      121—122 132 135 157
Thermionic emission from metals      212—216 230
Thermodynamic limit      9 62 307 308 309 310
Thermodynamic pressure      14—15 54 94 131 137
Thermodynamic temperature      12
Third law of thermodynamics      13 28 54—55 108 201
Thomas — Fermi model of the atom      6 223—227 231
Transfer matrix method      367 377 408 409 449
Transport phenomena      470 484
Tricritical point      363
Two-fluid model of superfluidity      165 182 278
Universality      344 345—346 354 435 442
Universality classes      344 347—348 359 398 404 413 439—440 442
Ursell functions      see "Cluster functions"
van der Waals equation of state      6 27 241 259 307 310—312
Vapor pressure of a solid      99
Vector models      365 372—377 398 404
Virial coefficients      159—160 197 239—245 248 249—253 259 260 261
Virial expansion of the equation of state      159 197 239 247 359
Virial theorem      65—66 85 86 231 490
viscosity      465 493
Viscous drag      464 471
Vortex motion in a Bose liquid      see "Quantized circulation in a Bose fluid"
Watson functions      393 413 510—512
Weiss theory of ferromagnetism      315 322—327 see
White dwarf stars      219—223
Wiedemann — Franz law      209 212
Wien's distribution law      170
Wiener — Khintchine theorem      452 474—478 491—492
work function      214 217
X-ray scattering by a fluid      458—459
X-Y model      316—317 404—405
Yang-Lee theory of condensation      310
Zero-point energy of a Bose system      271 276 300
Zero-point energy of a Fermi system      198 227 230 293 301
Zero-point energy of a solid      173 191
Zero-point pressure of a Bose system      271 276 300
Zero-point pressure of a Fermi system      199 220—221 230 293 301
Zero-point susceptibility of a Fermi system      203 205 209
Zeros of the grand partition function      310
Zeroth law of thermodynamics      28
Zeta function      506—507

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