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acoustic mode, 104 closed orbits, 168
adiabatic approximation, 125 coherence length, 198, 235
collective excitations, 3
adiabatic local density approximation, 205
Aharonov“Bohm phase, 335, 348, 371 commutator, 60, 79
Aharonov“Casher e¬ect, 332 composite fermion, 358, 379
Anderson Hamiltonian, 399 condensate, 236
anharmonic oscillator, 81 condensation energy, 244
annihilation operator conductance quantization, 319
for bosons, 78 conduction band, 132
for electrons, 30, 35 conductivity
for magnons, 119 electrical, 288, 299
for phonons, 96, 101 thermal, 304
anticommutation, 37 contact resistance, 324
anyon, 365 Cooper pair, 225
core state, 143
correlation energy, 49, 192
ballistic limit, 319
correlation potential, 192
band index, 130
Coulomb blockade, 336
band structure, 128
creation operator
basis vector, 99
for bosons, 78
BCS Hamiltonian, 235
for electrons, 30, 35
Berry™s phase, 371
for magnons, 119
Bloch electron, 125
for phonons, 96
velocity of, 160
Curie temperature, 121
Bloch™s theorem, 127
current density functional theory, 205
Bogoliubov theory of helium, 88
current density operator, 161, 256
Bogoliubov“Valatin transformation, 237
cyclotron frequency, 168, 345
Boltzmann equation, 285, 287
cyclotron mass, 168, 221
Born approximation, 172
Born“Oppenheimer approximation, 125
dangerous diagrams, 90
Bose“Einstein condensation, 87
Darwin term, 154
Bose“Einstein distribution (see boson, distribution
Debye model, 105
function)
Debye temperature, 106
boson, 31, 78
density functional theory, 183
distribution function, 86
time-dependent, 200
boundary conditions, periodic, 28, 97, 267
density of states
Bravais lattice, 99
electron, 131
Brillouin“Wigner perturbation theory, 52, 138
phonon, 104
Brillouin zone, 100, 130
density operator, 59
dielectric constant, 69, 76
canonical transformation, 224 dimerization, 218
channel, 320 Dirac equation, 114, 153


411
412 Index
Dirac notation, 27 Hall coe¬cient, 297
Drude formula, 335 Hall e¬ect, 20, 297
Hall ¬eld, 20
edge states, 353, 355 harmonic approximation, 96
e¬ective mass, 141, 180 harmonic oscillator, 80
Einstein model, 107, 117 Hartree“Fock approximation, 48, 71, 75, 125
heat“current density, 304
elastic mean free path, 315
electrical conductivity (see conductivity, electrical) heavy fermion, 385, 398
electron pairs, 84, 225, 236 Heisenberg model, 118
electron“phonon interaction, 17, 210“231, 299 Helmholtz energy, 113, 275, 282
electronic speci¬c heat, 221, 251 heterojunction, 318
elementary excitations, 1 Hohenberg“Kohn theorem, 182, 184
energy current, 304 hole-like behavior, 142
energy gap, 233, 243 hole state, 16, 68
ensemble density functional theory, 206 hole surface, 135
equation of continuity, 256, 286 Holstein“Primako¬ transformation, 116, 118
exchange-correlation energy functional, 189 Hubbard term, 399
exchange-correlation hole, 194 Hund™s rules, 384
exchange-correlation kernel, 205
exchange-correlation potential, 190 incompressibility, 343
exchange energy, 47, 223 inelastic scattering, 299
insulator, 132
exchange hole, 194
exchange phase, 364 intermediate state of superconductor, 272
exchange scattering, 47 inverse-e¬ective-mass tensor, 141, 168, 180
excitation Ising model, 118
isotope e¬ect, 235, 251
collective, 3
elementary, 1
quasiparticle, 3 Jahn“Teller e¬ect, 279
exciton, 180 jellium, 43
Johnson noise, 330
Exclusion Principle, 3, 15, 18, 143, 288, 301
extended zone scheme, 131 Jones zone, 156, 180
Josephson e¬ect, 265, 270
Fermi“Dirac distribution (see fermion, distribution
function) Kohler™s rule, 296
Fermi energy, 132 Kohn anomaly, 215
fermion, 32 Kohn“Sham formulation, 187
distribution function, 86 Kohn“Sham orbitals, 190
¬eld operator, 57 Korringa“Kohn“Rostoker method, 152
Fermi surface, 15, 133 Kondo e¬ect, 385
ferrimagnetism, 121 Kondo limit, 385
ferromagnetism, 10, 71, 117 Kondo temperature, 396
Feynman“Bijl formula, 369 Kronecker delta, 27
Fibonacci chain, 176
¬lling factor, 345 Lagrangian, 112
¬‚ux quantization, 265 Landau gauge, 344
Fock space, 33 Landau level, 345
Foldy“Wouthuysen transformation, 114, 153 Landauer“Buttiker formalism, 324, 356
¨
fractional statistics, 364 lattice vibration (see phonon)
Friedel sum rule, 174 Laughlin wavefunction, 358
Frohlich Hamiltonian, 210 linear chain, 4, 7, 94
¨
frozen phonon calculation, 197 Liouville equation, 286
Fuchs“Sondheimer theory, 294 liquid helium, 88
functional, 184 local density approximation, 191
derivative, 203 local spin density approximation, 197
London equation, 255
generalized gradient approximation, 198 longitudinally polarized phonon, 101
Ginzburg“Landau equations, 271, 277 Lorentz force, 111, 167
golden mean, 176 Lorenz number, 306
grand canonical ensemble, 85
Green™s-function method, 152 magnetic breakdown, 170
ground state, superconducting, 243 magnetic length, 345
group velocity, 6, 109, 161 magnetic moments, 113
413
Index
magnetoresistance, 296, 314 electron density, 187
magneto-roton, 368 phonon, 7, 101
magnon, 10, 117 (see also spin wave) polaron, 219
magnon interactions, 121 Poisson noise, 330
magnon“phonon interactions, 123 positron, 16
mass enhancement, 221 probable occupation number, 285
mass“velocity term, 153, 181 pseudoboson, 80
Matthiessen™s rule, 303 pseudogap region, 280
mean ¬eld, 117 pseudopotential, 148
mean free path, 292
Meissner e¬ect, 233, 254, 271 quantized ¬‚ux, 269, 346
mesoscopic system, 316 quantum Hall e¬ect, 19, 342
metallic ferromagnets, 71 quasicrystal, 174
mixed state, 235, 274 quasihole, 361
mobility gap, 351 quasiparticle, 3, 17, 363
Mossbauer e¬ect, 22 quenching, 114
¨
Mott insulator, 280
mu¬n tin potential, 152 random phase approximation, 60, 64
Rayleigh“Schrodinger perturbation theory, 52
¨
Nakajima Hamiltonian, 226 reciprocal lattice, 99
nearly-free-electron approximation, 136 reduced zone scheme, 131
Nielsen“Taylor e¬ect, 404 re¬‚ection probability, 322
N-process, 109 relativistic e¬ect, 153
number operator relaxation time, 292
for bosons, 79 anisotropic, 252
for fermions, 37 remapped free-electron model, 135, 150
repeated zone scheme, 136
occupation number representation, 32 reservoir, 320
Onsager relations, 311 resistance minimum, 385
optical mode, 103, 122 resistance quantum, 336
OPW (see orthogonalized plane wave) resistivity (see conductivity)
OPW method, 150 rigid-ion approximation, 210
orbit, 168 RKKY interaction, 384
periodic open, 169 Runge“Gross theorem, 201
orthogonalized plane wave, 146, 153
sandwichium, 139
´
Pade approximants, 191 scattering by impurities, 170
paramagnon, 74 scattering matrix, 320
Pauli Exclusion Principle (see Exclusion Principle) Schrie¬er“Wol¬ transformation, 400
Pauli spin susceptibility, 221 Schrodinger equation, 26
¨
Peierls transition, 218 screening, 13, 65
Peltier e¬ect, 308 second quantization, 34, 39, 78
penetration depth, 233, 255, 258 Seebeck e¬ect, 311
Penrose tile, 174 self-consistent Kohn“Sham scheme, 190
Perdew“Burke“Ernzerhof theory, 200 shot noise, 330
Perdew“Zunger parametrization, 192 simple metal, 146
periodic Anderson model, 400 single-mode approximation, 369
periodic boundary conditions, 28, 97, 267 singular value decomposition, 328
periodic open orbit, 169 skymion, 370
perturbation theory, 51 Slater determinant, 32
phase breaking length, 316 soliton, 7, 218
phase breaking time, 334 Sommerfeld gas, 46
phase shift, 152 sound velocity in metals, 19, 229
phonon, 7, 93“110 speci¬c heat
phonon drag, 312 due to phonons, 104
phonon interactions, 23, 107 electronic, 221, 251
plasma frequency spin, 48, 114
electron, 14, 64 spin-orbit coupling, 153, 157
ion, 12 spin raising and lowering operators, 115
plasma oscillation, 11, 64 spin wave, 11, 71 (see also magnon)
plasmon, 12, 14 strong-coupling superconductor, 243
polarization structure factor, 156
414 Index
superconductivity, 232“284 uncertainty principle, 53, 213, 271
super¬‚uid, 92 U-process (see Umklapp scattering)
symmetric gauge, 344 universal conductance ¬‚uctuation, 335

thermal conductivity, 304
thermoelectric e¬ects, 308 vacuum state, 30
thermoelectric power, absolute, 311 valence band, 132
thermopower, 311 vector mean free path, 293
tight-binding approximation, 144 Voronoy polyhedron, 178
T-matrix, 172 vortex rings, 93
Toda chain, 8 v-representability, 207
trace of operator, 84
transition matrix, 172
transition metals, 150, 302 weak-coupling superconductor, 243
transition temperature of superconductor, 247 weak localization, 332
transmission probability, 322 Wiedemann“Franz law, 306
transverse-even voltage, 297 Wigner crystal, 191
transversely polarized phonon, 101 Wilson ratio, 398
tunneling, 258“265 winding number, 370
type I superconductor, 233, 275
type II superconductor, 233, 275 Yukawa potential, 64, 70

ultrasonic attenuation, 252 Zener breakdown, 167
Umklapp scattering, 109

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