Авторизация
Поиск по указателям
Zagoskin A.M. — Quantum theory of many-body systems
Обсудите книгу на научном форуме Нашли опечатку?
Название: Quantum theory of many-body systemsАвтор: Zagoskin A.M. Аннотация: Intended for graduate students in physics and related fields, this text is a self contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green's functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory, and the Matsubara, Keldysh, and Nambu-Gor'kov formalisms. The aim is not to be exhaustive, but to present just enough detail to enable the student to follow the current research literature or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout their volume, and which therefore provides an ideal testing ground for many-body theories.
Язык: Рубрика: Физика /Квантовая теория поля /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1998Количество страниц: 229Добавлена в каталог: 10.10.2005Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Abel regularization 69 action 13 ff. Adiabatic hypothesis 68 Aharonov — Bohm effect 20 Andreev, and Josephson current 191 194 195 Andreev, levels in an SNS junction 190 ff. Andreev, reflection 184 ff. Annihilation operator 34—37 43—46 163 Anomalous average 155 Autocorrelation function 114 Autocovariation function 114 Bardeen — Cooper — Schrieffer (BCS) Hamiltonian 154 160 161 Bare particle 5 7 BBGKY chain 54 Bethe — Salpeter equation 91 ff. 158 Bloch, equation 102 Bloch, functions 50 Bogoliubov — de Gennes equations 163 ff. 184 Bogoliubov — de Gennes equations, functional 162 Bogoliubov — de Gennes equations, transformation 163 ff. Bogolon 164 166 Bose — Einstein, distribution function 102 Bose — Einstein, statistics 32 Bound state formation 149 158 Callen — Welton formula 115 Cancellation theorem 75 108 canonical ensemble 54 55 Cauchy theorem 64 65 110 Charging energy 203 206 208 Chronological ordering operator see “Time ordering operator” Closure relation 17 18 Coherence factors 165 166 Coherence length in normal metal 190 Collision integral 128 135 Commutation (anticommutation) relations, between phase and number operators 41 Commutation (anticommutation) relations, Bose 37 38 Commutation (anticommutation) relations, Fermi 45 Completeness see “Closure relation” Conductance 134 212 214 215 Conductance, quantization 133 ff. Continual integral see “Path integral” Contraction 70 Cooper effect 150 Cooper pair 43 150 154 157 185 206 Coulomb, blockade 203 ff. Coulomb, potential 2 Coulomb, potential, screening 3 4 145 Creation operator 34—37 43—46 163 Debye — Huckel screening length 4 145 Debye, frequency 148 Density matrix see “Statistical operator” Density operator 37 Dirac 14 23 Dirac, bra and ket vectors 17 Dressed particle 5 Dyson, equation for Green’s functions 82 126 170 Dyson, equation for the vertex part 89 Dyson, expansion 27 107 Electron-phonon collision integral 135 ff. Electron-phonon coupling constant 79 173 Elementary excitation see “Quasiparticle” Eliashberg equations 173 Evolution operator 23 ff. 103 Fermi — Dirac statistics 32 Fermi, distribution function 102 Fermi, surface 51 52 61 150 154 159 Feynman, diagrams 8 29 30 66 72 106 Feynman, rules 2 9 30 68 76—79 85 108 169 171 Field operators 37 45 Field operators, equations of motion 49 50 165 Fluctuation-dissipation theorem 114ff. Flux quantum 22 Fock space 31 Functional 13 162 Functional integrals see “Path integrals” Gaussian integral 12 17 19 161 Generalized force 112 Generalized susceptibility 113 Gibbs 55 97 Gor’kov’s equations 173 ff. 175 Gradient expansion 126 178 grand canonical ensemble 54 55 Grand potential 55 Grand potential, of the superconductor 167 Grand potential, of the superconductor, and Josephson current 193 194 Green’s function 8 11 49 Green’s function, advanced 12 62 63 97 99 202 Green’s function, analytic properties 57 97 174 Green’s function, and observables 65 179 Green’s function, causal 53 98 174 Green’s function, n-particle 85 86 Green’s function, nonequilibrium 117 ff. 175 201 202 Green’s function, of two operators 112 Green’s function, retarded 11 87 99 174 202 Green’s function, temperature (Matsubara) 104 ff. 175 176 Hamiltonian function 16 18 Hartree — Fock approximation 86 87 172 Heaviside step function 11 Heisenberg, equations of motion 26 68 103 165 Heisenberg, representation 26—28 56 Hilbert space 33 Hooke’s law 111 Huygens principle 9 Impedance 116 Indistinguishability principle 32 Instantaneous eigenstates 27 28 Interaction representation 26 68 107 Johnson — Nyquist noise 117 Josephson, coupling energy 207 Josephson, current 192 195 202 207 208 Josephson, effect 139 156 192 Josephson, effect, in a long SNS junction 195 Josephson, effect, in a quantum point contact 192 Josephson, effect, in an SND junction 199 Josephson, frequency 201 Kallen — Lehmann representation 58 64 98 131 174 197 Keldysh, contour 119 Keldysh, equations 126 Keldysh, formalism 121 ff. 102 175 200 Keldysh, function 121 125 201 Kramers — Kronig relation 65 99 Kubo formula 110 ff. 113 Kubo — Martin — Schwinger identity 115 Ladder approximation for the polarization operator 84 85 Ladder approximation for the two-particle Green’s function 93 158 Lagrange function 13 20 Landau 51 182 Landauer formula 133 ff. 143 211 Linear response theory 99 110 Liouville equation 97 Mass operator 81 Matsubara, conjugate 103 Matsubara, field operator 103 175 Matsubara, formalism 99 102 175 Matsubara, frequencies 105 108 110 Matsubara, frequencies, summation formulae 108 ff. Matsubara, Green’s function see “Green’s function” Mean field approximation (MFA) 2 155 156 161 202 203 Meromorphic function 60 Mesoscopic system 19 20 215 Mixed state 95 Nambu operators 169 Nambu — Gor’kov formalism 168 ff. Nambu — Gor’kov Green’s function 169 201 Normal ordering 70 Number, operator 36 Number-phase uncertainty relation 41 ff. Nyquist theorem 117 Occupation number 33 Off-diagonal long-range order (ODLRO) 155 Ohm’s Law 111 Pairing, Hamiltonian see “BCS Hamiltonian” Pairing, in superconducting state 150 Pairing, of field operators see “Contraction” Pairing, potential 150 170 185 186 Parity, effect 156 206 207 Parity, of permutation 44 Partial current 132 161 Partial summation of Feynman diagrams 82 172 Path integrals 13 14 161 Pauli matrices 122 170 Pauli principle 33 Perturbation expansion in many-body theory 66 106 Perturbation expansion in one-body theory 22 28 Phase of the superconducting order parameter 156 177 189 191 193 Phase, coherence length 20 Phase-number uncertainty relation 41 ff. Phonon 2 50 51 Phonon, Green’s function (propagator) 57 79 123 124 171 Plasma frequency 6 Plasmon 6 Plemelj theorem 65 Poisson summation formula 198 Polarization, insertion 83 Polarization, operator 83 144 Propagation function (propagator) 8 ff. 52 Propagation function (propagator), composition property 9 Propagation function (propagator), path integral expression 16 19 proximity effect 187 189 190 Pure state 95 Quantum coherence 156 190 Quantum kinetic equation 125 ff. 127 Quantum point contact (QPC), normal 128 Quantum point contact (QPC), superconducting 192 Quasiparticle 1 5 8 49 63 164 166 167 Quasiparticle, dispersion law 59 62 166 167 Quasiparticle, lifetime 50 64 Random phase approximation (RPA) 84 85 Renormalization of interactions 4 83 Riemann sum 16 S-operator (S-matrix) 17 25 27 52 68 69 107 Schrodinger equation 10 43 49 103 Schrodinger representation 23 screening 2—4 83 145 Second quantization 31 ff. Second quantization, representation of operators 37 38 45 46 Self energy part 78 136 172 Self energy part, irreducible 81 Self energy part, proper 81 Self-consistency relation 161 163 174 181 Sharvin resistance 132 ff. Single-electron tunneling (SET) 203 ff. Slater determinant 33 43 SND junction 199 SNS junction 195 ff. 115 Spectral density of fluctuations 114 Spectral density of Green’s function 100 174 Spectral density of Green’s function 63 99 Spontaneous symmetry breaking 156 157 Statistical operator 53 55 95 Sum rule 100 Superconducting order parameter 156 177 179 181 183 189 Superconducting order parameter, in a current-carrying state 176 ff. Superfluid velocity 176 Temperature Green’s function see “Green’s function” Temperature ordering operator 104 Thomas — Fermi equation 3 Thomas — Fermi screening length 3 84 Time ordering operator 24 Time ordering operator, in imaginary time see “Temperature ordering operator” Time ordering operator, on Keldysh contour 119 Transition amplitude 9 20 52 Transition probability 13 14 20 22 Tunneling Hamiltonian 139 ff. 200 Two-particle excitations 85 87 158 VACUUM 34 148 Vector potential 20 177 Vertex function 90—93 Virtual particle-hole pair 84 Watson’s lemma 12 64 Weierstrass formula 60 98 197 Wick’s rotation 103 104 Wick’s theorem 69 70 108 169 Wiener — Khintchin theorem 114 Wigner function 125 Yukawa potential 4 5 84 “Jelly” model 2—4
Реклама
|
|
О проекте