| preface ix . chapter 1 semiclassical introduction 1 1.1 elementary excitations 1 1.2 phonons 4 1.3 solitons 7 1.4 magnons 10 1.5 plasmons 12 1.6 electron quasiparticles 15 1.7 the electron-phonon interaction 17 1.8 the quantum hall effect 19 problems 22 chapter 2 second quantization and the electron gas 26 2.1 a single electron 26 2.2 occupation numbers 31 2.3 second quantization for fermions 34 2.4 the electron gas and the hartree-fock approximation 42 2.5 perturbation theory 50 2.6 the density operator 56 2.7 the random phase approximation and screening 60 2.8 spin waves in the electron gas 71 .problems 75 chapter 3 boson systems 78 3.1 second quantization for bosons 78 3.2 the harmonic oscillator 80 3.3 quantum statistics at finite temperatures 82 3.4 bogoliubov's theory of helium 88 3.5 phonons in one dimension 93 3.6 phonons in three dimensions 99 3.7 acoustic and optical modes 102 3.8 densities of states and the debye model 104 3.9 phonon interactions 107 3.10 magnetic moments and spin 111 3.11 magnons 117 problems 122 chapter 4 one-electron theory 125 4.1 bloch electrons 125 4.2 metals, insulators, and semiconductors 132 4.3 nearly free electrons 135 4.4 core states and the pseudopotential 143 4.5 exact calculations, relativistic effects, and the structure factor 150 4.6 dynamics of bloch electrons 160 4.7 scattering by impurities 170 4.8 quasicrystals and glasses 174 problems 179 chapter 5 density functional theory 182 5.1 the hohenberg-kohn theorem 182 5.2 the kohn-sham formulation 187 5.3 the local density approximation 191 5.4 electronic structure calculations 195 5.5 the generalized gradient approximation 198 5.6 more acronyms: tddft, cdft, and edft 200 problems 207 chapter 6 electron-phonon interactions 210 6.1 the frbhlich hamiltonian 210 6.2 phonon frequencies and the kohn anomaly 213 6.3 the peierls transition 216 6.4 polarons and mass enhancement.. 219 6.5 the attractive interaction between electrons 222 6.6 the nakajima hamiltonian 226 problems 230 chapter 7 superconductivity 232 7.1 the superconducting state 232 7.2 the bcs hamiltonian 235 7.3 the bogoliubov-valatin transformation 237 7.4 the ground-state wave function and the energy gap 243 7.5 the transition temperature 247 7.6 ultrasonic attenuation 252 7.7 the meissner effect 254 7.8 tunneling experiments 258 7.9 flux quantization and the josephson effect 265 7.10 the ginzburg-landau equations 271 7.11 high-temperature superconductivity 278 problems 282 chapter 8 semiclassical theory of conductivity in metals 285 8.1 the boltzmann equation 285 8.2 calculating the conductivity of metals 288 8.3 effects in magnetic fields 295 8.4 inelastic scattering and the temperature dependence of resistivity 299 8.5 thermal conductivity in metals 304 8.6 thermoelectric effects 308 problems 313 chapter 9 mesoscopic physics 315 9.1 conductance quantization in quantum point contacts 315 9.2 multi-terminal devices: the landauer-buttiker formalism 324 9.3 noise in two-terminal systems 329 9.4 weak localization 332 9.5 coulomb blockade 336 problems 339 chapter 10 the quantum hall effect 342 10.1 quantized resistance and dissipationless transport 342 10.2 two-dimensional electron gas and the integer quantum hall effect 10.3 edge states 353 10.4 the fractional quantum hall effect 357 10.5 quasiparticle excitations from the laughlin state 361 10.6 collective excitations above the laughlin state 367 10.7 spins 370 10.8 composite fermions 376 problems 380 chapter 11 the kondo effect and heavy fermions 383 11.1 metals and magnetic impurities 383 11.2 the resistance minimum and the kondo effect 385 11.3 low-temperature limit of the kondo problem 391 11.4 heavy fermions 397 problems 403 bibliography 405 index... 411 |
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