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Cover Art
PRINTED BOOKS
Author Bruus, Henrik.

Title Many-body quantum theory in condensed matter physics : an introduction / Henrik Bruus, Karsten Flensberg.

Published Oxford : Oxford University Press, 2004.

Copies

Location Call No. Status
 UniM ERC  530.41 BRUU    DUE 14-01-20
Physical description xix, 435 pages ; 24 cm.
Series Oxford graduate texts.
Oxford graduate texts.
Bibliography Includes bibliographical references and index.
Contents 1 First and second quantization 1 -- 1.1 First quantization, single-particle systems 2 -- 1.2 First quantization, many-particle systems 4 -- 1.3 Second quantization, basic concepts 10 -- 1.4 Second quantization, specific operators 18 -- 1.5 Second quantization and statistical mechanics 26 -- 2 Electron gas 32 -- 2.1 Non-interacting electron gas 33 -- 2.2 Electron interactions in perturbation theory 40 -- 2.3 Electron gases in 3, 2, 1 and 0 dimensions 45 -- 3 Phonons; coupling to electrons 52 -- 3.1 Jellium oscillations and Einstein phonons 52 -- 3.2 Electron-phonon interaction and the sound velocity 53 -- 3.3 Lattice vibrations and phonons in 1D 54 -- 3.4 Acoustical and optical phonons in 3D 57 -- 3.5 Specific heat of solids in the Debye model 59 -- 3.6 Electron-phonon interaction in the lattice model 61 -- 3.7 Electron-phonon interaction in the jellium model 64 -- 4 Mean-field theory 66 -- 4.1 Basic concepts of mean-field theory 66 -- 4.2 Art of mean-field theory 69 -- 4.3 Hartree-Fock approximation 70 -- 4.4 Broken symmetry 72 -- 4.5 Ferromagnetism 74 -- 5 Time dependence in quantum theory 80 -- 5.1 Schrodinger picture 80 -- 5.2 Heisenberg picture 81 -- 5.3 Interaction picture 81 -- 5.4 Time-evolution in linear response 84 -- 5.5 Time-dependent creation and annihilation operators 84 -- 5.6 Fermi's golden rule 86 -- 5.7 T-matrix and the generalized Fermi's golden rule 87 -- 5.8 Fourier transforms of advanced and retarded functions 88 -- 6 Linear response theory 92 -- 6.1 General Kubo formula 92 -- 6.2 Kubo formula for conductivity 95 -- 6.3 Kubo formula for conductance 97 -- 6.4 Kubo formula for the dielectric function 99 -- 7 Transport in mesoscopic systems 103 -- 7.1 S-matrix and scattering states 104 -- 7.2 Conductance and transmission coefficients 109 -- 7.3 Electron wave guides 114 -- 8 Green's functions 121 -- 8.1 "Classical" Green's functions 121 -- 8.2 Green's function for the one-particle Schrodinger equation 121 -- 8.3 Single-particle Green's functions of many-body systems 125 -- 8.4 Measuring the single-particle spectral function 132 -- 8.5 Two-particle correlation functions of many-body systems 136 -- 9 Equation of motion theory 140 -- 9.1 Single-particle Green's function 140 -- 9.2 Single level coupled to continuum 142 -- 9.3 Anderson's model for magnetic impurities 143 -- 9.4 Two-particle correlation function 149 -- 10 Transport in interacting mesoscopic systems 152 -- 10.1 Model Hamiltonians 152 -- 10.2 Sequential tunneling: the Coulomb blockade regime 154 -- 10.3 Coherent many-body transport phenomena 159 -- 10.4 Conductance for Anderson-type models 162 -- 10.5 Kondo effect in quantum dots 169 -- 11 Imaginary-time Green's functions 184 -- 11.1 Definitions of Matsubara Green's functions 187 -- 11.2 Connection between Matsubara and retarded functions 189 -- 11.3 Single-particle Matsubara Green's function 192 -- 11.4 Evaluation of Matsubara sums 193 -- 11.5 Equation of motion 197 -- 11.6 Wick's theorem 198 -- 11.7 Example: polarizability of free electrons 201 -- 12 Feynman diagrams and external potentials 204 -- 12.1 Non-interacting particles in external potentials 204 -- 12.2 Elastic scattering and Matsubara frequencies 206 -- 12.3 Random impurities in disordered metals 208 -- 12.4 Impurity self-average 211 -- 12.5 Self-energy for impurity scattered electrons 216 -- 13 Feynman diagrams and pair interactions 226 -- 13.1 Perturbation series for G 227 -- 13.2 Feynman rules for pair interactions 228 -- 13.3 Self-energy and Dyson's equation 233 -- 13.4 Feynman rules in Fourier space 233 -- 13.5 Examples of how to evaluate Feynman diagrams 236 -- 13.6 Cancellation of disconnected diagrams, general case 239 -- 13.7 Feynman diagrams for the Kondo model 241 -- 14 Interacting electron gas 246 -- 14.1 Self-energy in the random phase approximation 246 -- 14.2 Renormalized Coulomb interaction in RPA 250 -- 14.3 Groundstate energy of the electron gas 253 -- 14.4 Dielectric function and screening 256 -- 14.5 Plasma oscillations and Landau damping 260 -- 15 Fermi liquid theory 266 -- 15.1 Adiabatic continuity 266 -- 15.2 Semi-classical treatment of screening and plasmons 269 -- 15.3 Semi-classical transport equation 272 -- 15.4 Microscopic basis of the Fermi liquid theory 278 -- 16 Impurity scattering and conductivity 285 -- 16.1 Vertex corrections and dressed Green's functions 286 -- 16.2 Conductivity in terms of a general vertex function 291 -- 16.3 Conductivity in the first Born approximation 293 -- 16.4 Conductivity from Born scattering with interactions 296 -- 16.5 Weak localization correction to the conductivity 298 -- 16.6 Disordered mesoscopic systems 308 -- 17 Green's functions and phonons 313 -- 17.1 Green's function for free phonons 313 -- 17.2 Electron-phonon interaction and Feynman diagrams 314 -- 17.3 Combining Coulomb and electron-phonon interactions 316 -- 17.4 Phonon renormalization by electron screening in RPA 319 -- 17.5 Cooper instability and Feynman diagrams 322 -- 18 Superconductivity 325 -- 18.1 Cooper instability 325 -- 18.2 BCS groundstate 327 -- 18.3 Microscopic BCS theory 329 -- 18.4 BCS theory with Matsubara Green's functions 331 -- 18.5 Nambu formalism of the BCS theory 335 -- 18.6 Gauge symmetry breaking and zero resistivity 341 -- 18.7 Josephson effect 343 -- 19 1D electron gases and Luttinger liquids 347 -- 19.1 What is a Luttinger liquid? 347 -- 19.2 Experimental realizations of Luttinger liquid physics 348 -- 19.3 A first look at the theory of interacting electrons in 1D 348 -- 19.4 Spinless Luttinger-Tomonaga model 352 -- 19.5 Bosonization of the Tomonaga model Hamiltonian 357 -- 19.6 Electron operators in bosonized form 363 -- 19.7 Green's functions 368 -- 19.8 Measuring local density of states by tunneling 369 -- 19.9 Luttinger liquid with spin 373 -- A Fourier transformations 376 -- A.1 Continuous functions in a finite region 376 -- A.2 Continuous functions in an infinite region 377 -- A.3 Time and frequency Fourier transforms 377 -- A.4 Some useful rules 377 -- A.5 Translation-invariant systems 378.
Other author Flensberg, Karsten.
Subject Condensed matter.
Many-body problem.
Quantum theory.
ISBN 0198566336 (hbk.) £45.00