Morandi G. — Statistical Mechanics: An Intermediate Course :: Электронная библиотека попечительского совета мехмата МГУ

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Morandi G. — Statistical Mechanics: An Intermediate Course

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Название: Statistical Mechanics: An Intermediate Course

Автор: Morandi G.

Аннотация:

Discussing the foundations of both classical and quantum statistical mechanics, this book aims to bridge a gap that exists between standard textbooks on the subject and more advanced books. It is devised for a one-semester course on statistical mechanics at the graduate level. Its prerequisite is therefore a more elementary course on the same subject. Emphasis is laid on the geometrical aspects of classical thermodynamics, on the foundational problems, and on selected applications, mainly to spin systems, the meaning of quantum statistics, phase transitions, critical phenomena and the renormalization group.

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Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 583

Добавлена в каталог: 18.10.2010

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Предметный указатель

$\lambda$ -transition      449
$\mathbf{SO}(3)$       210 ff
$\mathbf{SU}(2)$       210 ff
$\Theta$ -vacua      457 ff
Absolute temperature      8 11
Action-angle variables      66—68
Adiabatic compressibility      24
Adiabatic walls      3
Andronikashvili's experiment      450
Annihilation operators      280 ff
Anomalous dimension      375 379
Antiferromagnetism      354 358
Antisymmetrizer      277
Attraction manifold      438
Auxiliary fields      170 343
Baker — Campbell — Hausdorff formula      149
Bipartite lattice      358
Bloch equations      162
Block spin Hamiltonians      4 70 483
Bogoliubov inequality      215—216 389
Bogoliubov model      453 ff
Bogoliubov transformation      455
Bohr — van Leeuwen theorem      117
Bose gas      §14
Bose — Einstein condensation      310 ff
Boson coherent states      460
Braid groups      272 ff
canonical ensemble      §6 244
Canonical transformations      54
Caratheodory      44 48
Causal response function      152 336
Characters      269
Charts      13 App.A
chemical potential      9
Clausius — Clapeyron equation      367—368
Clausius' theorem      9
Codimension      521
Commutator subgroup      269
Compatibility conditions      40
Complete integrability      63 ff
Complete set of commuting observables      220 226
Complete vector fields      50 527
Complex projective space $\mathbf{CP^{n}}$       221
Concave function      25
Conjugate variable      11
Connection form      221
Conservative system      49
Constant of the motion      63
Continuous transitions      370
Convex function      25
Convex hull      233
Convex linear combination      230
Coordination number      174
Correlation functions      61—62 §7 §15
correlation length      375 378
Cotangent bundle      49 530
Creation operators      230
Critical exponents      §19
Critical field      429 435 440
Critical points      365
Critical surface      433
Critical temperature      491
Cumulant expansions      496 ff
Curie temperature      357
Cycles      67
Cyclic vectors      227
de Broglie wavelength      93
Decomposition of KMS states      390
Density matrix      228 ff
Density of states      75 303
Derivation      52
Dimensional analysis      425 ff
Dirac picture      128 334
Dynamic susceptibility      336
Ehrenfest classification      370
Empirical temperature      8
entropy      2 10 88 122 246 248
Equation(s) of state      4 11 109 300
Equipartition theorem      95 ff 103
Ergodic theory      71 ff
Euclidean action      175 344
Euclidean group $\mathbf{E}(3)$       126
Euclidean group $\mathbf{E}(3)$ , canonical lift      128
Euclidean time      342
Euler's theorem      13
Exact differential      9 34
Exponent inequalities      413 ff
Extensive      4
Fermi energy      304
Fermi function      299
Fermi gas      §14
Fermi momentum      305
Fermi surface      305
ferromagnetism      322 ff 357
Field operators      283 ff
First homology group      269
First homotopy group      see "Fundamental g"
First law      8
First-order phase transitions      370 438
Fixed points      485 ff 489
Fluctuation-dissipation theorem      155 ff 337
Fluctuations      374 ff 435
Flux quantization      444
Flux quantum      439
Fock space      246 §13
Foliation      35 70
Fountain effect      450
Frobenius' Theorem      41
Functional derivative      145 ff
Functional integral      342 ff
Fundamental domains      27
Fundamental equation      14
Fundamental group      264
Gap      434
Gauge group      203
Gauge invariance      289 ff
Gaussian identity      169
Gaussian model      392 ff
Generalized homogeneous functions      415
Generating function      55
Generating functional      144 348
Gibbs free energy      18
Gibbs — Duhem relation      14
Gibbs' paradox      86 92
Gibbs' phase rule      364
Ginsburg — Landau equations      441 ff
Ginsburg — Landau functional      439
Ginsburg — Landau parameter      446
Ginsburg — Landau theory      439 ff
Ginzburg criterion      435 ff
Goldstone boson      448
Goldstone theorem      §11 §18
Grand potential      19 108 247
Grand-canonical ensemble      §6 246
Hamilton's equations      49
Hamiltonian flow      50
Hartree — Fock equations      320 ff
Heisenberg model      160 430
Heisenberg picture      58 240
Heisenberg's equations      240
Helicity      315
Helmoltz free energy      17
Higgs mechanism      440
High- $T_{c}$ superconductivity      433
homogeneous functions      12
Homogeneous spaces      209
Homotopy      67
Hopf bundle      211 221 259
Hyperscaling      417
Identical particles      §13

Inequivalent quantizations      266 ff
Inequivalent representations      290
Integrating factor      9 37
Intensive      4
Invariant area element      74
Invariant tori      64
Involution      63
Irreducible set      237
Irreversible processes      3
Irrotational flow      452
Ising model      160 166 402 419 §26
Isolating integrals      72
Isothermal compressibility      24
Isotropy subgroup      see "Little g"
Jacobi identity      52
Jensen's inequality      173
Joint density of states      89
Joint simple spectrum      227
Kadanoff's block scaling      §24
Kam theorem      70 ff
Kelvin temperature      see "Absolute t"
Kernel      36
KMS conditions      251 ff
Landau criterion for superfluidity      453
Landau theory of phase transitions      §20
Latent heat      366
Lee — Yang theorems      381 ff
Legendre transform      17
Leibnitz rule      52
Lie algebras      52 App.A
Lie brackets      52 App.A
Lie derivative      51 App.A
Lie series      52 App.A
Lifting homotopy theorem      268
Linear differential forms      see "One-forms"
Linear response theory      148 ff 334
Linearized RG equations      485
Liouville equation      61
Liouville integrability theorem      64
Liouville operator      53
Liouville theorem      55
Little group      208
London equation      437
London penetration depth      437
London theory of superconductivity      486 ff
Lower critical field      485
Manifold      5 App.A
Matsubara frequencies      852
Maxwell relations      20 ff
Mean field approximation      §9 §16
Mechanocaloric effect      450
Meissner — Ochsenfeld effect      434 448
Mermin — Wagner theorem      §11 §18
Metric transitivity      76
Micro canonical ensemble      §5
Mixing      82
Momentum Space Renormalization Group      §27
Momentum-space rescaling      478 ff
Multiply connected      264
Occupation number      278
One-form      8 App.A
One-particle density matrix      294
One-particle operators      284 ff
Operator ordering      288
Order parameter      204 209 382
Orientable manifold      36
Ornstein — Zernike theory      377 ff
Parallel transport      221
Paramagnetic bodies      30 ff
Parity      131 ff
Partition function      §6 245
Path integrals      see "Functional integrals"
Path-connected      13
Pfaffian equations      14 36 47
phase diagram      365 372
Phase equilibrium      364
Phase space      49
Phase-space averages      80
Phases      364
Phonons in $He^{II}$       451
Plemelj formula      153
Poisson brackets      51 ff 162
Poisson's theorem      63
Pomeranchuk's stability criterion      329
Pre-Hilbert spaces      57
Projectable Quantum Mechanics      268 ff
Projective Hilbert space      221
projectors      221
Pure states      221 ff
Quasi-static processes      3
Quasiparticle Vacua      see " $\Theta$ -vacua"
Quasiparticles in $He^{II}$       455
Random variables      222 ff
Real space renormalization group      §26
Real space rescaling      476 ff
Rectilinear diameters (law of)      412
Reduction of the wave packet      223
Regular foliation      35
Reversible processes      3
Rotons      451
Sackur — Tetrode formula      93
Scaling exponents      416
Scaling fields      436
Scaling hypothesis      415
Scaling laws      413
Schroedinger picture      53 ff 239
Schroedinger's equation      236
Second law      9 ff
Second sound      452
Second virial coefficient      114 302 310
Second-order transitions      370
Semigroup      478
Simple spectrum      227
Simply connected      13 264
Slater determinant      278
Sommerfeld expansion      304
Spectral families      225 App.B
Spherical model      400 ff
Spin waves      §10 360
Spin-density waves      359
Spontaneous symmetry breaking (SSB)      §11 §18
Staggered magnetization      359
Statistical average      229
Statistical ensemble      229
Statistical operator      see "Density matrix"
Stieltjes' integral      223
Stirling's formula      88
Stone — Von Neumann theorem      58 App.B
Strong continuity      223
Structure factor      143
Structure function      75
Sublattice magnetization      359
Submanifold      5 App.A
Superconductivity      see "Ginsburg — Landau Theory"
Superfluid current      451 463
Superfluid density      452
Superfluidity      §22
Superselection rules      238 291
Superselection sectors      238 271
Symmetrizer      276
Symmetry groups      203
Symplectic group $\mathbf{Sp(n)}$       56
Thermal expansion coefficient      28
Thermal Hartree — Fock approximation (THFA)      318 ff
Thermal wavelength      93
Thermodynamic limit      1—4 §18
Thermodynamic potentials      §2
Third law      10
Time averages      80
Time reversal      131 133

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