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Zagoskin A.M. Quantum theory of many-body systems
Zagoskin A.M.  Quantum theory of many-body systems







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: Quantum theory of many-body systems

: Zagoskin A.M.

:

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.


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ed2k: ed2k stats

: 1998

: 229

: 10.10.2005

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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      3437 4346 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      3437 4346 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 Greens 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 7679 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
Gorkovs 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
Greens function      8 11 49
Greens function, advanced      12 62 63 97 99 202
Greens function, analytic properties      57 97 174
Greens function, and observables      65 179
Greens function, causal      53 98 174
Greens function, n-particle      85 86
Greens function, nonequilibrium      117 ff. 175 201 202
Greens function, of two operators      112
Greens function, retarded      11 87 99 174 202
Greens 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      2628 56
Hilbert space      33
Hookes 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 Greens 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, Greens function      see Greens 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 Gorkov formalism      168 ff.
Nambu Gorkov Greens 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
Ohms 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, Greens 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      24 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 Greens function $\Gamma$      100 174
Spectral density of Greens function $\rho$      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 Greens function      see Greens 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      9093
Virtual particle-hole pair      84
Watsons lemma      12 64
Weierstrass formula      60 98 197
Wicks rotation      103 104
Wicks theorem      69 70 108 169
Wiener Khintchin theorem      114
Wigner function      125
Yukawa potential      4 5 84
Jelly model      24
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