<< . .

. 77
( : 78)



. . >>

(1960), 696].
[38] U. Eckern, J. Low Temp. Phys., 62 (1986), 525.
[39] A. A. Abrikosov and L. P. Gor™kov, Zh. Eksp. Teor. Fiz., 39 (1960), 1781 [Sov.
Phys. JETP, 12 (1961), 1243].
[40] A. L. Shelankov, J. Low Temp. Phys., 60 (1985), 29.
[41] K. S. Usadel, Phys. Rev. Lett., 25 (1970), 507.
[42] K. E. Gray, ed., Nonequilibrium Superconductivity, Phonons, and Kapitza
Boundaries (New York: Plenum Press, 1981).
[43] A. Schmid (1981), Kinetic equations for dirty superconductors. (Included in ref-
erence [42].)
[44] I. Schuller and K. E. Gray, Solid State Commun., 23 (1977), 337.
[45] A. Schmid and G. Sch¨n, Phys. Rev. Lett., 43 (1979), 793.
o
[46] A. Schmid and G. Sch¨n, J. Low Temp. Phys., 20 (1975), 207.
o
[47] J. Clarke (1981), Charge imbalance. (Included in reference [42].)
[48] D. N. Langenberg and A. I. Larkin, eds., Nonequilibrium Superconductivity (El-
sevier Science Publishers B.V., 1986).
[49] N. B. Kopnin, Theory of Nonequilibrium Superconductivity (Oxford: Oxford
University Press, 2001).
[50] J. Schwinger, Proc. Nat. Acad. Sci., 37 (1951), 452.
[51] K. B. Efetov, Adv. Phys., 32 (1983), 53.
[52] R. Jackiw, Phys. Rev. D, 9 (1974), 1686.
[53] J. M. Cornwall, R. Jackiw and E. Tomboulis, Phys. Rev. D, 10 (1974), 2428.
[54] E. Lundh and J. Rammer, Phys. Rev. A, 66 (2002), 033607.
[55] N. N. Bogoliubov, J. Phys. (Moscow), 11 (1947), 23.

[56] E. P. Gross, Nuovo Cimento, 20 (1961), 454; J. Math. Phys., 4 (1963), 195.
[57] L. P. Pitaevskii, Zh. Eksp. Teor. Fiz., 40 (1961), 646 [Sov. Phys. JETP, 13
(1961), 451].
[58] S. T. Beliaev, Zh. Eksp. Teor. Fiz., 34 (1958), 417 [Sov. Phys. JETP, 7 (1958),
289].
[59] S. T. Beliaev, Zh. Eksp. Teor. Fiz., 34 (1958), 433 [Sov. Phys. JETP, 7 (1958),
299].
526 References


[60] V. N. Popov and L. D. Faddeev, Zh. Eksp. Teor. Fiz., 47 (1964), 1315 [Sov.
Phys. JETP, 20 (1965), 890].
[61] V. N. Popov, Zh. Eksp. Teor. Fiz., 47 (1964), 1759 [Sov. Phys. JETP, 20 (1965),
1185].

[62] V. N. Popov, Functional Integrals and Collective Excitations (New York: Cam-
bridge University Press, 1987).
[63] M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A.
Cornell, Science, 269 (1995), 198.
[64] O. Penrose and L. Onsager, Phys. Rev., 104 (1956), 576.
[65] F. Dalfovo and S. Stringari, Phys. Rev. A, 53 (1996), 2477.
[66] N. P. Proukakis, S. A. Morgan, S. Choi, and K. Burnett, Phys. Rev. A, 58
(1998), 2435.
[67] G. Baym and C. J. Pethick, Phys. Rev. Lett., 76 (1996), 6.
[68] F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Rev. Mod. Phys., 71
(1999), 463.
[69] S. Stenholm, Phys. Rev. A, 57 (1998), 2942.
[70] S. Inouye, M. R. Andrews, J. Stenger, H.-J. Miesner, D. M. Stamper-Kurn, and
W. Ketterle, Nature, 392 (1998), 151.
[71] P. W. Anderson, Phys. Rev., 102 (1958), 1008.
[72] E. Abrahams, P. W. Anderson, D. C. Licciardello and T. V. Ramakrishnan,
Phys. Rev. Lett., 42 (1979), 673. Reprinted in P. W. Anderson, Basic Notions
of Condensed Matter Physics (Benjamin-Cummings, 1984).
[73] F. Wegner, Z. Phys. B, 25 (1976), 327.
[74] D. J. Thouless in Ill Condensed Matter, R. Balian, R. Maynard, and G. Toulouse,
eds., Les Houches, Session XXXI (North-Holland, 1987).
[75] N. F. Mott and W. D. Twose, Adv. Phys., 10 (1961), 107.
[76] R. Landauer, Philos. Mag., 21 (1970), 863.
[77] V. L. Berezinskii, Zh. Eksp. Teor. Fiz., 65 (1973), 1251 [Sov. Phys. JETP, 38
(1974), 620].
[78] A. A. Abrikosov and I. A. Ryzhkin, Adv. Phys., 27 (1978), 147.
[79] N. F. Mott, in Electronics and structural properties of amorphous semiconduc-
tors, P. G. Le Comber and J. Mort, eds. (London: Academic Press, 1973).
[80] J.S. Langer and T. Neal, Phys. Rev. Lett., 16 (1966), 984.
References 527


[81] K. M. Watson, J. Math. Phys., 10 (1969), 688.
[82] A. I. Larkin and D. E. Khmel™nitskii, Usp. Fyz. Nauk., 136 (1982), 536 [Sov.
Phys. Usp., 25 (1982), 185].
[83] D. E. Khmelnitskii, Physica B, 126 (1984), 235.
[84] B. L. Al™tshuler, V. E. Kravtsov and I. V. Lerner in Mesoscopic Phenomena
in Solids, B. L. Al™tshuler, P. A. Lee, and R. A. Webb, eds. (North-Holland:
Elsevier Science Publishers B.V., 1991).
[85] D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys., 66 (1994), 261.
[86] L. P. Gor™kov, A. I. Larkin and D. E. Khmel™nitskii, Pis™ma Zh. Eksp. Teor.
Fiz., 30 (1979), 1251 [Sov. Phys. JETP Lett., 30 (1979), 228].
[87] J. Rammer and A. Schmid, Destruction of phase coherence by electron-phonon
interaction in disordered conductors. Contributed paper to the International
Conference on Localization, Interaction and Transport Phenomena, Braun-
schweig, Abstracts p. 155 (1984.) (or NORDITA preprint-85/39 (1985)).
[88] G. Bergmann, Phys. Rep., 107 (1984), 1.
[89] B. L. Al™tshuler, A. G. Aronov, M. E. Gershenson and Yu. V. Sharvin, Sov. Sci.
Rev. A. Phys., 9 (1987), 223 (I. M. Khalatnikov, ed.).
[90] J. Rammer and A. Schmid, Phys. Rev. B, 34 (1986), 1352.
[91] J. Rammer, A. L. Shelankov and A. Schmid, Phys. Rev. Lett., 60 (1988), 1985
(C).
[92] K. S. Il™in, N. G. Ptitsina, A.V. Sergeev et al., Phys. Rev. B, 57 (1998), 15623.
[93] A. Schmid, Z. Phys., 259 (1973), 421.
[94] B. L. Al™tshuler, A. G. Aronov and D. E. Khmel™nitskii, J. Phys. C, 15 (1982),
7367.
[95] J. Rammer and A. L. Shelankov, Phys. Rev. B, 36 (1987), 3135.
[96] I. S. Gradstheyn and I. M. Ryzhik, Table of Integrals, Series and Products (New
York: Academic Press, 1980).
[97] A. Kawabate, J. Phys. Soc. Japan, 53 (1984), 3540.
[98] H.-P. Wittmann and A. Schmid, J. Low Temp. Phys., 69 (1987), 131.
[99] B. L. Al™tshuler and A. G. Aronov, Zh. Eksp. Teor. Fiz., 77 (1979), 2028 [Sov.
Phys. JETP, 50 (1979), 968].
[100] I. L. Bronevoi, Zh. Eksp. Teor. Fiz., 79 (1980), 1936. [Sov. Phys. JETP, 52
(1980), 977]
528 References


[101] I. L. Bronevoi, Zh. Eksp. Teor. Fiz., 83 (1982), 338 [Sov. Phys. JETP, 56
(1982), 185].
[102] B. L. Al™tshuler and A. G. Aronov in Electron“Electron Interactions in Disor-
dered Systems, A. L. Efros and M. Pollak, eds. ( North-Holland: Elsevier Science
Publishers B.V., 1985).
[103] A. Schmid, Z. Physik, 271 (1974), 251.
[104] B. L. Al™tshuler and A. G. Aronov, Zh. Eksp. Teor. Fiz., 75 (1978), 1610 [Sov.
Phys. JETP, 48 (1978), 812].
[105] B. L. Al™tshuler and A. G. Aronov, Pis™ma Zh. Eksp. Teor. Fiz., 30 (1979),
514 [Sov. Phys. JETP Lett., 30 (1979), 482].
[106] R. A. Serota, S. Feng, C. Kane and P. A. Lee, Phys. Rev. B, 36 (1987), 5031.
[107] B. L. Al™tshuler and B. I. Shklovskii, Zh. Eksp. Teor. Fiz., 91 (1986), 220 [Sov.
Phys. JETP, 64 (1986), 127].
[108] B. L. Al™tshuler and D. E. Khmel™nitskii, Pis™ma Zh. Eksp. Teor. Fiz., 42
(1985), 291 [Sov. Phys. JETP Lett., 42 (1985), 359].
[109] P. A. Lee, A. D. Stone and H. Fukuyama, Phys. Rev. B, 35 (1987), 1039.
[110] B. L. Al™tshuler, Pis™ma Zh. Eksp. Teor. Fiz., 41 (1985), 530 [Sov. Phys. JETP
Lett., 41 (1985), 648].
[111] P. A. Lee and A. D. Stone, Phys. Rev. Lett., 55 (1985), 1622.
[112] B. L. Al™tshuler, V. E. Kravtsov and I. V. Lerner, Pis™ma Zh. Eksp. Teor. Fiz.,
43 (1986), 342 [Sov. Phys. JETP Lett., 43 (1986), 441].
[113] B. L. Al™tshuler and B. Z. Spivak, Pis™ma Zh. Eksp. Teor. Fiz., 42 (1985), 363
[Sov. Phys. JETP Lett., 42 (1985), 447].
[114] S. Feng, P. A. Lee and A. D. Stone, Phys. Rev. Lett., 56 (1986), 1960; 56
(1986), 2772 (E).
[115] S. Washburn and A. Webb, Adv. Phys., 35 (1986), 375.
[116] P. Shen (ed.), Scattering and Localization of Classical Waves in Random Media
(World Scienti¬c, 1989).
[117] D. Forster, D. R. Nelson and M. J. Stephen, Phys. Rev. A, 16 (1977), 732.
[118] P. C. Martin, E. D. Siggia and H. A. Rose, Phys. Rev. A, 8 (1973), 423.

[119] H. K. Janssen, Z. Phys. B, 23 (1976), 377.
[120] R. Bausch, H. K. Janssen and H. Wagner, Z. Phys. B, 24 (1976), 113.
[121] C. De Dominicis, Phys. Rev. B, 18 (1978), 4913.
References 529


[122] P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys., 49 (1977), 435.
[123] S. F. Edwards and P. W. Anderson, J. Phys. (Paris) F, 5 (1975), 965.
[124] A. A. Abrikosov, Zh. Eksp. Teor. Fiz., 32 (1957), 1422 [Sov. Phys. JETP, 5
(1957), 1174].
[125] J. Bardeen and M. J. Stephen, Phys. Rev., 140 (1965), A1197.
[126] A. Schmid, Phys. Kondensierten Materie, 5 (1966), 302.
[127] C. Caroli and K. Maki, Phys. Rev., 159 (1967), 306.
[128] C. R. Hu and R. S. Thompson, Phys. Rev. B, 6 (1972), 110.
[129] M. Tinkham, Introduction to Superconductivity, 2nd edition (McGraw-Hill,
1996).
[130] G. Blatter, M. V. Feigel™man, V. B. Geshkenbein, A. I. Larkin and V. M.
Vinokur, Rev. Mod. Phys., 66 (1994), 1125.
[131] A. Schmid and W. Hauger, J. Low Temp. Phys., 11 (1973), 667.

[132] A. L. Larkin and Yu. N. Ovchinnikov, Zh. Eksp. Teor. Fiz., 65 (1973), 1704
[Sov. Phys. JETP, 38 (1974), 854].
[133] J. M¨llers and A. Schmid, Ann. Physik, 4 (1995), 757.
u
[134] S. Grundberg and J. Rammer, Phys. Rev. B, 61 (2000), 699.
[135] C. R. Werner and U. Eckern, Ann. Physik, 6 (1997), 595.
[136] E. H. Brandt, Rep. Prog. Phys., 58 (1995), 1465.
[137] E. H. Brandt, Int. J. Mod. Phys. B, 5 (1999), 751.
[138] Wu Liu, T. W. Clinton and C. J. Lobb, Phys. Rev. B, 52 (1995), 7482.
[139] S. Bhattacharya and M. J. Higgins, Phys. Rev. Lett., 70 (1993), 2617.
[140] W. K. Kwok, J. A. Fendrich, C. J. van der Beek and G. W. Crabtree, Phys.
Rev. Lett., 73 (1994), 2614.
[141] U. Yaron, P. L. Gammel, D. A. Huse et al., Nature, 376 (1995), 753.
[142] M. C. Hellerqvist, D. Ephron, W. R. White, M. R. Beasley and A. Kapitulnik,
Phys. Rev. Lett., 76 (1996), 4022.
[143] M. J. Higgins and S. Bhattacharya, Physica C, 257 (1996), 232.
[144] M. Marchevsky, J. Aarts, P. H. Kes and M. V. Indenbom, Phys. Rev. Lett., 78
(1997), 531.
[145] A. E. Koshelev and V. M. Vinokur, Phys. Rev. Lett., 73 (1994), 3580.
530 References


[146] S. Scheidl and V. M. Vinokur, Phys. Rev. B, 57 (1998), 13800.
[147] S. Scheidl and V. M. Vinokur, Phys. Rev. E, 57 (1998), 2574.
[148] J. Kierfeld, T. Nattermann and T. Hwa, Phys. Rev. B, 55 (1997), 626.
[149] J. M. Caillol, D. Levesque, J. J. Weis and J. P. Hansen, J. Stat. Phys., 28
(1982), 325.
[150] J. M. Kosterlitz and D. J. Thouless, J. Phys. C, 6 (1973), 1181.
[151] D. S. Fisher, Phys. Rev. B, 22 (1980), 1190.
[152] P. A. M. Dirac, Physik. Zeits. Sowjetunion, 3 (1933), 64. Reprinted in J.
Schwinger, ed., Selected Papers on Quantum Electrodynamics (New York: Dover
Publications, 1958).
[153] P. Ao and J. Rammer, Phys. Rev. B, 43 (1991), 5397.
[154] R. P. Feynman and F. L. Vernon, Annals of Physics, 24 (1963), 118.
[155] R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (New
York: McGraw-Hill, 1965).
[156] A. Schmid, J. Low Temp. Phys., 49 (1982), 609.
[157] A. O. Caldeira and A. J. Leggett, Physica, 121A (1983), 587.
Index

Abrikosov ¬‚ux lattice, 461 Bose“Einstein condensation, 51, 301, 351,
Abrikosov“Shubnikov phase, 461 353
absorption vertex, 129 Bose“Einstein distribution, 73, 98
action, 306, 321, 325 bosons, 6
free, 317 Brownian motion, 194, 450
adiabatic switching, 83
canonical ensemble, 49, 70
adjoint operator, 8
grand, 50, 70
analytical continuation, 142
canonical formulation, 281
analytical properties of the free propaga-
central limit theorem, 329
tor, 521
charge imbalance, 250
annihilation operator
charge-density wave, 231
bose, 23
chemical potential, 50
fermion, 16
classical electrodynamics, 28
anti-time-ordering, 56
classical equation of motion, 310, 511
antisymmetric subspace, 9
classical ¬eld, 297
appendix contour, 91
closed contour, 85
Aristotelian dynamics, 449
closed time path, 84
auxiliary ¬eld, 453
coherence length, 231, 368
average ¬eld, 297
coherent backscattering, 384, 387
BCS-energy gap, 220 collision integral
BCS-pairing, 219 electron“phonon, 208
BCS-state, 39 electron-electron, 214
BCS-theory, 217, 219 electron-impurity, 188
Bogoliubov equations, 364 collision rate, 435
Bogoliubov“Valatin transformation, 221 commutator, 3
Boltzmann conductivity, 377 condensate density, 356
Boltzmann equation, 188 condensate wave function, 353, 363
Boltzmann factor, 323 condensation energy, 221
Boltzmann propagator, 193, 412 conductance, 159
Boltzmannian paths, 401 conductance ¬‚uctuations, 442
Boltzmannian motion, 192 conductance tensor, 159
path of, 192 conductivity, 191
bose ¬eld, 24 minimum metallic, 377
Bose function, 98 conductivity diagram, 161
Bose gas, 351 conductivity diagrams, 377
Bose“Einstein condensate, 51, 77 conductivity tensor, 158


531
532 Index


continuity equation, 13, 14, 191, 195 Drude theory, 190
contour ordered Green™s function dual space, 9
inverse free, 105 dyadic notation, 467
contour ordering, 85, 88 dynamic melting, 493
contour variable, 87 Dyson equation, 116
Cooperon, 379, 381, 390 equilibrium, 138
Cooperon equation, 403 left-right subtracted, 179
creation operator matrix, 135
bose, 23 non-equilibrium, 303
fermion, 14 Dyson equations
critical phenomena, 258, 290 non-equilibrium, 116
critical velocity, 493 Dyson™s formula, 84
current correlation function, 169 Dyson“Beliaev equation, 357
current density, 13, 40, 63, 67 Dyson“Schwinger equation, 279
current response, 155
e¬ective action, 296, 299, 323
current response function, 155
two-particle irreducible, 343
current vertex, 157
Eilenberger equations, 232
cyclotron frequency, 215
Einstein relation, 244
elastic medium, 26
d™Alembertian, 27
electric ¬eld ¬‚uctuations, 172
Debye cut-o¬, 59
electron“electron interaction
Debye model, 26
di¬usion enhanced, 436
deformation potential, 46, 410
electron“hole excitations, 112
delta functional, 314
electron“phonon interaction, 45, 46, 200,
density, 67
410
probability, 13
electron“photon Hamiltonian, 48
density matrix, 22, 48, 56
electron“photon interaction, 48
density operator, 38
emission vertex, 129
current, 40
energy, 56
density response, 153
energy gap, 220, 222
density response function, 153
energy relaxation rate, 431, 435, 436
density“density response, 434
Euclidean action, 197, 506
diamagnetic current, 40
evolution operator, 3, 55
dielectric function, 434
exact impurity eigenstates, 430
di¬usion approximation, 194
exclusion principle, 16, 18, 21
di¬usion constant, 194, 198
di¬usion equation, 196
Fermi energy, 22
di¬usion propagator, 194, 196
Fermi ¬eld, 21
Di¬uson, 197, 381, 382, 401, 431
Fermi function, 98
diluteness parameter, 351
Fermi gas, 22
dirty superconductor, 242
Fermi momentum, 37
displacement ¬eld, 26, 27, 410
Fermi sea, 22, 111
dissipation, 169
Fermi surface, 22
distribution function, 187
Fermi wavelength, 231, 232, 377
distribution functions for superconductors,
Fermi™s Golden Rule, 168
245
Fermi“Dirac distribution, 73
Index 533


fermion“boson interaction, 45, 107, 125 full, 118
fermions, 6 grand canonical, 72
Feynman rules, 113 Greater, 64
Feynman-Vernon theory, 510 imaginary time, 140
¬eld, 297 inverse, 66
¬‚uctuation“dissipation relation, 180 kinetic, 67, 72
¬‚uctuation“dissipation theorem, 70, 72, Lesser, 63
171, 450 matrix, 122
¬‚ux ¬‚ow regime, 462 one-particle, 22
¬‚ux quantum, 427 phonon, 66
Fock space, 15 quasi-classical, 199
free energy, 50, 290 retarded, 66, 513
free particle density of states, 522 single-particle, 62
free particle propagator, 515 symmetric matrix, 280
functional derivative, 272 time-ordered, 65, 81
functional determinant, 317 trajectory, 240
functional integral, 314 two-particle, 64
restricted, 330 Green™s function technique
functional integration, 313 standard diagrammatic impurity, 377
fundamental dynamic equation, 279 Green™s operator
advanced, 517
gauge invariance, 14 retarded, 517
gauge transformation, 231 Green™s operators, 515, 518
Gaussian integral, 315
Hamilton™s function, 61, 504
Gell-Mann“Low theorem, 83
generating functional, 69, 103, 270, 281, Hamiltonian, 3, 36
grand canonical, 72
317, 320
Hartree approximation, 470
generator of 1PI-vertices, 299
generator of connected amplitudes, 284, Hartree diagrams, 110
Heisenberg picture, 57
290
generator of connected Green™s functions, hermitian conjugation, 318
hermitian operator, 9
322
high-temperature superconductors, 476
generator of cumulants, 290
Ginzburg“Landau regime, 247
identical particles, 6
Gorkov equations, 224
imaginary-time, 140
gradient approximation, 184
imaginary-time formalism, 140
Grassmann ¬eld, 319
imaginary-time propagator, 506, 515
Grassmann algebra, 282
impurity correlator, 106
Grassmann variable, 282, 319
impurity scattering, 188
function of a, 319
inelastic di¬erential cross section, 175
Green™s function, 4, 62
inelastic scattering rate, 409
advanced, 67
in¬‚uence functional, 508
anomalous, 224, 357
interaction picture, 82
anti-time-ordered, 65
inverse propagator, 261
closed time path, 87
irreducible vertex functions
contour ordered, 87, 90
one-particle, 298
534 Index


Jacobian, 316, 459 mean free path, 193
jellium model, 45 Meissner e¬ect, 460
Johnson noise, 172 melting curve, 496
Joule heating, 169 mesoscopic ¬‚uctuations, 442
mesoscopic sample, 437
Kadano¬“Baym equations, 148 metal“insulator transition, 373, 376

<< . .

. 77
( : 78)



. . >>