Many-body quantum theory in condensed matter physics: an introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2007
|
| Ausgabe: | Reprint. |
| Schriftenreihe: | Oxford graduate texts
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 435 S. Ill., graph. Darst. |
| ISBN: | 0198566336 9780198566335 |
Internformat
MARC
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| 100 | 1 | |a Bruus, Henrik |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Many-body quantum theory in condensed matter physics |b an introduction |c Henrik Bruus and Karsten Flensberg |
| 246 | 1 | 3 | |a Many body quantum theory in condensed matter physics |
| 250 | |a Reprint. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2007 | |
| 300 | |a XIX, 435 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford graduate texts | |
| 650 | 4 | |a Vielkörperproblem - Kondensierte Materie - Quantenmechanisches System | |
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| 650 | 0 | 7 | |a Festkörperphysik |0 (DE-588)4016921-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Festkörperphysik |0 (DE-588)4016921-2 |D s |
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| 689 | 1 | 2 | |a Quantenfeldtheorie |0 (DE-588)4047984-5 |D s |
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| 700 | 1 | |a Flensberg, Karsten |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015681612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804136562759303168 |
|---|---|
| adam_text | CONTENTS
List of symbols
xiv
1
First and second quantization
1
1.1
First quantization, single-particle systems
2
1.2
First quantization, many-particle systems
4
1.2.1
Permutation symmetry and indistinguishability
5
1.2.2
The single-particle states as basis states
6
1.2.3
Operators in first quantization
8
1.3
Second quantization, basic concepts
10
1.3.1
The occupation number representation
10
1.3.2
The boson creation and annihilation operators
10
1.3.3
The fermion creation and annihilation operators
13
1.3.4
The general form for second quantization operators
14
1.3.5
Change of basis in second quantization
16
1.3.6
Quantum field operators and their Fourier transforms
17
1.4
Second quantization, specific operators
18
1.4.1
The harmonic oscillator in second quantization
18
1.4.2
The electromagnetic field in second quantization
19
1.4.3
Operators for kinetic energy, spin, density
and current
21
1.4.4
The Coulomb interaction in second quantization
23
1.4.5
Basis states for systems with different kinds
of particles
25
1.5
Second quantization and statistical mechanics
26
1.5.1
Distribution function for non-interacting
fermions
29
1.5.2
Distribution function for non-interacting bosons
29
1.6
Summary and outlook
30
2
The electron gas
32
2.1
The non-interacting electron gas
33
2.1.1
Bloch theory of electrons in a static ion lattice
33
2.1.2
Non-interacting electrons in the jellium model
36
2.1.3
Non-interacting electrons at finite temperature
39
2.2
Electron interactions in perturbation theory
40
2.2.1
Electron interactions in first-order
perturbation theory
42
2.2.2
Electron interactions in second-order
perturbation theory
44
2.3
Electron gases in
3, 2, 1
and
0
dimensions
45
2.3.1 3D
electron gases: metals and semiconductors
45
2.3.2
2D electron gases: GaAs/GaAlAs heterostructures
47
vu
viii CONTENTS
2.3.3
ID electron gases: carbon nanotubes
49
2.3.4
OD
electron gases: quantum dots
50
2.4
Summary and outlook
51
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 ID
54
3.4
Acoustical and optical phonons in
3D 57
3.5
The 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
3.8
Summary and outlook
65
4
Mean-field theory
66
4.1
Basic concepts of mean-field theory
66
4.2
The art of mean-field theory
69
4.3
Hartree-Fock approximation
70
4.3.1
Hartree-Fock approximation for the homogenous
electron gas
71
4.4
Broken symmetry
72
4.5
Ferromagnetism
74
4.5.1
The
Heisenberg
model of ionic ferromagnets
74
4.5.2
The
Stoner
model of metallic ferromagnets
76
4.6
Summary and outlook
78
5
Time dependence in quantum theory
80
5.1
The
Schrödinger
picture
80
5.2
The
Heisenberg
picture
81
5.3
The 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
The
Т
-matrix and the generalized Fermi s golden rule
87
5.8
Fourier transforms of advanced and retarded functions
88
5.9
Summary and outlook
90
6
Linear response theory
92
6.1
The general
Kubo
formula
92
6.1.1
Kubo
formula in the frequency domain
94
6.2
Kubo
formula for conductivity
95
6.3
Kubo
formula for conductance
97
6.4
Kubo
formula for the dielectric function
99
6.4.1
Dielectric function for translation-invariant system
100
6.4.2
Relation between dielectric function and
conductivity
101
6.5
Summary and outlook
101
CONTENTS ix
7 Transport in
mesoscopic systems
103
7.1
The
«S-matrix
and scattering states
104
7.1.1 Definition
of the
¿ř-matrix
104
7.1.2
Definition of the scattering states
107
7.1.3
Unitarity of the ^-matrix
107
7.1.4
Time-reversal symmetry
108
7.2
Conductance and transmission coefficients
109
7.2.1
The
Landauer
formula, heuristic derivation
110
7.2.2
The
Landauer
formula, linear response derivation
112
7.2.3
The Landauer-Biittiker formalism for multiprobe
systems
113
7.3
Electron wave guides
114
7.3.1
Quantum point contact and conductance
quantization
114
7.3.2
The Aharonov-Bohm effect
118
7.4
Summary and outlook
119
8
Green s functions
121
8.1
Classical Green s functions
121
8.2
Green s function for the one-particle
Schrödinger
equation
121
8.2.1
Example: from the 5-matrix to the Green s function
124
8.3
Single-particle Green s functions of many-body systems
125
8.3.1
Green s function of translation-invariant systems
126
8.3.2
Green s function of free electrons
126
8.3.3
The
Lehmann
representation
128
8.3.4
The spectral function
130
8.3.5
Broadening of the spectral function
131
8.4
Measuring the single-particle spectral function
132
8.4.1
Tunneling spectroscopy
133
8.5
Two-particle correlation functions of many-body systems
136
8.6
Summary and outlook
139
9
Equation of motion theory
140
9.1
The single-particle Green s function
140
9.1.1
Non-
interacting particles
142
9.2
Single level coupled to continuum
142
9.3
Anderson s
modei
for magnetic impurities
143
9.3.1
The equation of motion for the Anderson model
145
9.3.2
Mean-field approximation for the Anderson model
146
9.4
The two-particle correlation function
149
9.4.1
The random phase approximation
149
9.5
Summary and outlook
151
10
Transport in interacting mesoscopic systems
152
10.1
Model Hamiltonians
152
x
CONTENTS
10.2
Sequential tunneling: the Coulomb blockade regime
154
10.2.1
Coulomb blockade for a metallic dot
155
10.2.2
Coulomb blockade for a quantum dot
158
10.3
Coherent many-body transport phenomena
159
10.3.1
Cotunneling
159
10.3.2
Inelastic cotunneling for a metallic dot
160
10.3.3
Elastic cotunneling for a quantum dot
161
10.4
The conductance for Anderson-type models
162
10.4.1
The conductance in linear response
163
10.4.2
Calculation of Coulomb blockade peaks
166
10.5
The Kondo effect in quantum dots
169
10.5.1
From the Anderson model to the Kondo model
169
10.5.2
Comparing the Kondo effect in metals and
quantum dots
173
10.5.3
Kondo-model conductance to second order in
Ну
174
10.5.4
Kondo-model conductance to third order in Hs
175
10.5.5
Origin of the logarithmic divergence
180
10.5.6
The Kondo problem beyond perturbation theory
181
10.6
Summary and outlook
182
11
Imaginary-time Green s functions
184
11.1
Definitions of Matsubara Green s functions
187
11.1.1
Fourier transform of Matsubara Green s functions
188
11.2
Connection between Matsubara and retarded functions
189
11.2.1
Advanced functions
191
11.3
Single-particle Matsubara Green s function
192
11.3.1
Matsubara Green s function for non-interacting
particles
192
11.4
Evaluation of Matsubara sums
193
11.4.1
Summations over functions with simple poles
194
11.4.2
Summations over functions with known branch cuts
196
11.5
Equation of motion
197
11.6
Wick s theorem
198
11.7
Example: polarizability of free electrons
201
11.8
Summary and outlook
202
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
12.3.1
Feynman diagrams for the impurity scattering
209
12.4
Impurity self-average
211
12.5
Self-energy for impurity scattered electrons
216
12.5.1
Lowest-order approximation
217
12.5.2
First-order Born approximation
217
12.5.3
The full Born approximation
220
CONTENTS xi
12.5.4
The self-consistent Born approximation and beyond
222
12.6
Summary and outlook
224
13
Feynman diagrams and pair interactions
226
13.1
The perturbation series for
Q
227
13.2
The Feynman rules for pair interactions
228
13.2.1
Feynman rules for the denominator of G(b,a)
229
13.2.2
Feynman rules for the numerator of Q{b, a)
230
13.2.3
The cancellation of disconnected Feynman diagrams
231
13.3
Self-energy and Dyson s equation
233
13.4
The Feynman rules in Fourier space
233
13.5
Examples of how to evaluate Feynman diagrams
236
13.5.1
The
Hartree
self-energy diagram
236
13.5.2
The Fock self-energy diagram
237
13.5.3
The pair-bubble self-energy diagram
238
13.6
Cancellation of disconnected diagrams, general case
239
13.7
Feynman diagrams for the Kondo model
241
13.7.1
Kondo model self-energy, second order in
J
243
13.7.2
Kondo model self-energy, third order in
J
244
13.8
Summary and outlook
245
14
The interacting electron gas
246
14.1
The self-energy in the random phase approximation
246
14.1.1
The density dependence of self-energy diagrams
247
14.1.2
The divergence number of self-energy diagrams
248
14.1.3
RPA
resummation of the self-energy
248
14.2
The renormalized Coulomb interaction in
RPA
250
14.2.1
Calculation of the pair-bubble
251
14.2.2
The electron-hole pair interpretation of
RPA
253
14.3
The groundstate energy of the electron gas
253
14.4
The dielectric function and screening
256
14.5
Plasma oscillations and Landau damping
260
14.5.1
Plasma oscillations and plasmons
262
14.5.2
Landau damping
263
14.6
Summary and outlook
264
15
Fermi liquid theory
266
15.1
Adiabatic continuity
266
15.1.1
Example: one-dimensional well
267
15.1.2
The quasiparticle concept and conserved quantities
268
15.2
Semi-classical treatment of screening and plasmons
269
15.2.1
Static screening
270
15.2.2
Dynamical screening
271
15.3
Semi-classical transport equation
272
15.3.1
Finite lifetime of the quasiparticles
276
xii CONTENTS
15.4 Microscopic
basis of the Fermi liquid theory
278
15.4.1
Renormalization of the single particle
Green s function
278
15.4.2
Imaginary part of the single-particle
Green s function
280
15.4.3
Mass renormalization?
283
15.5
Summary and outlook
283
16
Impurity scattering and conductivity
285
16.1
Vertex corrections and dressed Green s functions
286
16.2
The conductivity in terms of a general vertex function
291
16.3
The conductivity in the first Born approximation
293
16.4
Conductivity from Born scattering with interactions
296
16.5
The weak localization correction to the conductivity
298
16.6
Disordered mesoscopic systems
308
16.6.1
Statistics of quantum conductance,
random matrix theory
308
16.6.2
Weak localization in mesoscopic systems
309
16.6.3
Universal conductance fluctuations
310
16.7
Summary and outlook
312
17
Green s functions and phonons
313
17.1
The 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
17.3.1
Migdal s theorem
317
17.3.2
Jellium phonons and the effective electron-electron
interaction
318
17.4
Phonon renormalization by electron screening in
RPA
319
17.5
The Cooper instability and Feynman diagrams
322
17.6
Summary and outlook
324
18
Superconductivity
325
18.1
The Cooper instability
325
18.2
The BCS groundstate
327
18.3
Microscopic BCS theory
329
18.4
BCS theory with Matsubara Green s functions
331
18.4.1
Self-consistent determination of the BCS
order parameter
Дк
332
18.4.2
Determination of the critical temperature Tc
333
18.4.3
Determination of the BCS quasiparticle
density of states
334
18.5
The
Nambu
formalism of the BCS theory
335
18.5.1
Spinors and Green s functions in the
Nambu
formalism
335
18.5.2
The Meissner effect and the London equation
336
CONTENTS xiii
18.5.3
The vanishing paramagnetic current response in
BCS theory
337
18.6
Gauge symmetry breaking and zero resistivity
341
18.6.1
Gauge transformations
341
18.6.2
Broken gauge symmetry and dissipationless current
342
18.7
The
Josephson
effect
343
18.8
Summary and outlook
345
19
ID electron gases and Luttinger liquids
347
19.1
What is a Luttinger liquid?
347
19.2
Experimental realizations of Luttinger liquid physics
348
19.2.1
Example: Carbon Nanotubes
348
19.2.2
Example: semiconductor wires
348
19.2.3
Example: quasi ID materials
348
19.2.4
Example: Edge states in the fractional
quantum Hall effect
348
19.3
A first look at the theory of interacting electrons in ID
348
19.3.1
The quasiparticles in ID
350
19.3.2
The lifetime of the quasiparticles in ID
351
19.4
The
spinless
Luttinger-Tomonaga model
352
19.4.1
The Luttinger-Tomonaga model Hamiltonian
352
19.4.2
Inter-branch interaction
354
19.4.3
Intra-branch interaction and charge conservation
355
19.4.4
Umklapp processes in the half-filled band case
356
19.5
Bosonization of the Tomonaga model Hamiltonian
357
19.5.1
Derivation of the bosonized Hamiltonian
357
19.5.2
Diagonalization of the bosonized Hamiltonian
360
19.5.3
Real space representation
360
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
19.10
Summary and outlook
374
A Fourier transformations
376
A.I 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
Exercises
380
Bibliography
421
Index
424
|
| adam_txt |
CONTENTS
List of symbols
xiv
1
First and second quantization
1
1.1
First quantization, single-particle systems
2
1.2
First quantization, many-particle systems
4
1.2.1
Permutation symmetry and indistinguishability
5
1.2.2
The single-particle states as basis states
6
1.2.3
Operators in first quantization
8
1.3
Second quantization, basic concepts
10
1.3.1
The occupation number representation
10
1.3.2
The boson creation and annihilation operators
10
1.3.3
The fermion creation and annihilation operators
13
1.3.4
The general form for second quantization operators
14
1.3.5
Change of basis in second quantization
16
1.3.6
Quantum field operators and their Fourier transforms
17
1.4
Second quantization, specific operators
18
1.4.1
The harmonic oscillator in second quantization
18
1.4.2
The electromagnetic field in second quantization
19
1.4.3
Operators for kinetic energy, spin, density
and current
21
1.4.4
The Coulomb interaction in second quantization
23
1.4.5
Basis states for systems with different kinds
of particles
25
1.5
Second quantization and statistical mechanics
26
1.5.1
Distribution function for non-interacting
fermions
29
1.5.2
Distribution function for non-interacting bosons
29
1.6
Summary and outlook
30
2
The electron gas
32
2.1
The non-interacting electron gas
33
2.1.1
Bloch theory of electrons in a static ion lattice
33
2.1.2
Non-interacting electrons in the jellium model
36
2.1.3
Non-interacting electrons at finite temperature
39
2.2
Electron interactions in perturbation theory
40
2.2.1
Electron interactions in first-order
perturbation theory
42
2.2.2
Electron interactions in second-order
perturbation theory
44
2.3
Electron gases in
3, 2, 1
and
0
dimensions
45
2.3.1 3D
electron gases: metals and semiconductors
45
2.3.2
2D electron gases: GaAs/GaAlAs heterostructures
47
vu
viii CONTENTS
2.3.3
ID electron gases: carbon nanotubes
49
2.3.4
OD
electron gases: quantum dots
50
2.4
Summary and outlook
51
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 ID
54
3.4
Acoustical and optical phonons in
3D 57
3.5
The 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
3.8
Summary and outlook
65
4
Mean-field theory
66
4.1
Basic concepts of mean-field theory
66
4.2
The art of mean-field theory
69
4.3
Hartree-Fock approximation
70
4.3.1
Hartree-Fock approximation for the homogenous
electron gas
71
4.4
Broken symmetry
72
4.5
Ferromagnetism
74
4.5.1
The
Heisenberg
model of ionic ferromagnets
74
4.5.2
The
Stoner
model of metallic ferromagnets
76
4.6
Summary and outlook
78
5
Time dependence in quantum theory
80
5.1
The
Schrödinger
picture
80
5.2
The
Heisenberg
picture
81
5.3
The 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
The
Т
-matrix and the generalized Fermi's golden rule
87
5.8
Fourier transforms of advanced and retarded functions
88
5.9
Summary and outlook
90
6
Linear response theory
92
6.1
The general
Kubo
formula
92
6.1.1
Kubo
formula in the frequency domain
94
6.2
Kubo
formula for conductivity
95
6.3
Kubo
formula for conductance
97
6.4
Kubo
formula for the dielectric function
99
6.4.1
Dielectric function for translation-invariant system
100
6.4.2
Relation between dielectric function and
conductivity
101
6.5
Summary and outlook
101
CONTENTS ix
7 Transport in
mesoscopic systems
103
7.1
The
«S-matrix
and scattering states
104
7.1.1 Definition
of the
¿ř-matrix
104
7.1.2
Definition of the scattering states
107
7.1.3
Unitarity of the ^-matrix
107
7.1.4
Time-reversal symmetry
108
7.2
Conductance and transmission coefficients
109
7.2.1
The
Landauer
formula, heuristic derivation
110
7.2.2
The
Landauer
formula, linear response derivation
112
7.2.3
The Landauer-Biittiker formalism for multiprobe
systems
113
7.3
Electron wave guides
114
7.3.1
Quantum point contact and conductance
quantization
114
7.3.2
The Aharonov-Bohm effect
118
7.4
Summary and outlook
119
8
Green's functions
121
8.1
"Classical" Green's functions
121
8.2
Green's function for the one-particle
Schrödinger
equation
121
8.2.1
Example: from the 5-matrix to the Green's function
124
8.3
Single-particle Green's functions of many-body systems
125
8.3.1
Green's function of translation-invariant systems
126
8.3.2
Green's function of free electrons
126
8.3.3
The
Lehmann
representation
128
8.3.4
The spectral function
130
8.3.5
Broadening of the spectral function
131
8.4
Measuring the single-particle spectral function
132
8.4.1
Tunneling spectroscopy
133
8.5
Two-particle correlation functions of many-body systems
136
8.6
Summary and outlook
139
9
Equation of motion theory
140
9.1
The single-particle Green's function
140
9.1.1
Non-
interacting particles
142
9.2
Single level coupled to continuum
142
9.3
Anderson's
modei
for magnetic impurities
143
9.3.1
The equation of motion for the Anderson model
145
9.3.2
Mean-field approximation for the Anderson model
146
9.4
The two-particle correlation function
149
9.4.1
The random phase approximation
149
9.5
Summary and outlook
151
10
Transport in interacting mesoscopic systems
152
10.1
Model Hamiltonians
152
x
CONTENTS
10.2
Sequential tunneling: the Coulomb blockade regime
154
10.2.1
Coulomb blockade for a metallic dot
155
10.2.2
Coulomb blockade for a quantum dot
158
10.3
Coherent many-body transport phenomena
159
10.3.1
Cotunneling
159
10.3.2
Inelastic cotunneling for a metallic dot
160
10.3.3
Elastic cotunneling for a quantum dot
161
10.4
The conductance for Anderson-type models
162
10.4.1
The conductance in linear response
163
10.4.2
Calculation of Coulomb blockade peaks
166
10.5
The Kondo effect in quantum dots
169
10.5.1
From the Anderson model to the Kondo model
169
10.5.2
Comparing the Kondo effect in metals and
quantum dots
173
10.5.3
Kondo-model conductance to second order in
Ну
174
10.5.4
Kondo-model conductance to third order in Hs
175
10.5.5
Origin of the logarithmic divergence
180
10.5.6
The Kondo problem beyond perturbation theory
181
10.6
Summary and outlook
182
11
Imaginary-time Green's functions
184
11.1
Definitions of Matsubara Green's functions
187
11.1.1
Fourier transform of Matsubara Green's functions
188
11.2
Connection between Matsubara and retarded functions
189
11.2.1
Advanced functions
191
11.3
Single-particle Matsubara Green's function
192
11.3.1
Matsubara Green's function for non-interacting
particles
192
11.4
Evaluation of Matsubara sums
193
11.4.1
Summations over functions with simple poles
194
11.4.2
Summations over functions with known branch cuts
196
11.5
Equation of motion
197
11.6
Wick's theorem
198
11.7
Example: polarizability of free electrons
201
11.8
Summary and outlook
202
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
12.3.1
Feynman diagrams for the impurity scattering
209
12.4
Impurity self-average
211
12.5
Self-energy for impurity scattered electrons
216
12.5.1
Lowest-order approximation
217
12.5.2
First-order Born approximation
217
12.5.3
The full Born approximation
220
CONTENTS xi
12.5.4
The self-consistent Born approximation and beyond
222
12.6
Summary and outlook
224
13
Feynman diagrams and pair interactions
226
13.1
The perturbation series for
Q
227
13.2
The Feynman rules for pair interactions
228
13.2.1
Feynman rules for the denominator of G(b,a)
229
13.2.2
Feynman rules for the numerator of Q{b, a)
230
13.2.3
The cancellation of disconnected Feynman diagrams
231
13.3
Self-energy and Dyson's equation
233
13.4
The Feynman rules in Fourier space
233
13.5
Examples of how to evaluate Feynman diagrams
236
13.5.1
The
Hartree
self-energy diagram
236
13.5.2
The Fock self-energy diagram
237
13.5.3
The pair-bubble self-energy diagram
238
13.6
Cancellation of disconnected diagrams, general case
239
13.7
Feynman diagrams for the Kondo model
241
13.7.1
Kondo model self-energy, second order in
J
243
13.7.2
Kondo model self-energy, third order in
J
244
13.8
Summary and outlook
245
14
The interacting electron gas
246
14.1
The self-energy in the random phase approximation
246
14.1.1
The density dependence of self-energy diagrams
247
14.1.2
The divergence number of self-energy diagrams
248
14.1.3
RPA
resummation of the self-energy
248
14.2
The renormalized Coulomb interaction in
RPA
250
14.2.1
Calculation of the pair-bubble
251
14.2.2
The electron-hole pair interpretation of
RPA
253
14.3
The groundstate energy of the electron gas
253
14.4
The dielectric function and screening
256
14.5
Plasma oscillations and Landau damping
260
14.5.1
Plasma oscillations and plasmons
262
14.5.2
Landau damping
263
14.6
Summary and outlook
264
15
Fermi liquid theory
266
15.1
Adiabatic continuity
266
15.1.1
Example: one-dimensional well
267
15.1.2
The quasiparticle concept and conserved quantities
268
15.2
Semi-classical treatment of screening and plasmons
269
15.2.1
Static screening
270
15.2.2
Dynamical screening
271
15.3
Semi-classical transport equation
272
15.3.1
Finite lifetime of the quasiparticles
276
xii CONTENTS
15.4 Microscopic
basis of the Fermi liquid theory
278
15.4.1
Renormalization of the single particle
Green's function
278
15.4.2
Imaginary part of the single-particle
Green's function
280
15.4.3
Mass renormalization?
283
15.5
Summary and outlook
283
16
Impurity scattering and conductivity
285
16.1
Vertex corrections and dressed Green's functions
286
16.2
The conductivity in terms of a general vertex function
291
16.3
The conductivity in the first Born approximation
293
16.4
Conductivity from Born scattering with interactions
296
16.5
The weak localization correction to the conductivity
298
16.6
Disordered mesoscopic systems
308
16.6.1
Statistics of quantum conductance,
random matrix theory
308
16.6.2
Weak localization in mesoscopic systems
309
16.6.3
Universal conductance fluctuations
310
16.7
Summary and outlook
312
17
Green's functions and phonons
313
17.1
The 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
17.3.1
Migdal's theorem
317
17.3.2
Jellium phonons and the effective electron-electron
interaction
318
17.4
Phonon renormalization by electron screening in
RPA
319
17.5
The Cooper instability and Feynman diagrams
322
17.6
Summary and outlook
324
18
Superconductivity
325
18.1
The Cooper instability
325
18.2
The BCS groundstate
327
18.3
Microscopic BCS theory
329
18.4
BCS theory with Matsubara Green's functions
331
18.4.1
Self-consistent determination of the BCS
order parameter
Дк
332
18.4.2
Determination of the critical temperature Tc
333
18.4.3
Determination of the BCS quasiparticle
density of states
334
18.5
The
Nambu
formalism of the BCS theory
335
18.5.1
Spinors and Green's functions in the
Nambu
formalism
335
18.5.2
The Meissner effect and the London equation
336
CONTENTS xiii
18.5.3
The vanishing paramagnetic current response in
BCS theory
337
18.6
Gauge symmetry breaking and zero resistivity
341
18.6.1
Gauge transformations
341
18.6.2
Broken gauge symmetry and dissipationless current
342
18.7
The
Josephson
effect
343
18.8
Summary and outlook
345
19
ID electron gases and Luttinger liquids
347
19.1
What is a Luttinger liquid?
347
19.2
Experimental realizations of Luttinger liquid physics
348
19.2.1
Example: Carbon Nanotubes
348
19.2.2
Example: semiconductor wires
348
19.2.3
Example: quasi ID materials
348
19.2.4
Example: Edge states in the fractional
quantum Hall effect
348
19.3
A first look at the theory of interacting electrons in ID
348
19.3.1
The "quasiparticles" in ID
350
19.3.2
The lifetime of the "quasiparticles" in ID
351
19.4
The
spinless
Luttinger-Tomonaga model
352
19.4.1
The Luttinger-Tomonaga model Hamiltonian
352
19.4.2
Inter-branch interaction
354
19.4.3
Intra-branch interaction and charge conservation
355
19.4.4
Umklapp processes in the half-filled band case
356
19.5
Bosonization of the Tomonaga model Hamiltonian
357
19.5.1
Derivation of the bosonized Hamiltonian
357
19.5.2
Diagonalization of the bosonized Hamiltonian
360
19.5.3
Real space representation
360
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
19.10
Summary and outlook
374
A Fourier transformations
376
A.I 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
Exercises
380
Bibliography
421
Index
424 |
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| any_adam_object_boolean | 1 |
| author | Bruus, Henrik Flensberg, Karsten |
| author_facet | Bruus, Henrik Flensberg, Karsten |
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| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.17.P7 |
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| callnumber-subject | QC - Physics |
| classification_rvk | UL 1000 UP 1300 |
| classification_tum | PHY 602f PHY 026f |
| ctrlnum | (OCoLC)253857929 (DE-599)BVBBV022474176 |
| dewey-full | 530.41 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.41 |
| dewey-search | 530.41 |
| dewey-sort | 3530.41 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | Reprint. |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV022474176 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:45:48Z |
| indexdate | 2024-07-09T20:58:23Z |
| institution | BVB |
| isbn | 0198566336 9780198566335 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015681612 |
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| physical | XIX, 435 S. Ill., graph. Darst. |
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| spelling | Bruus, Henrik Verfasser aut Many-body quantum theory in condensed matter physics an introduction Henrik Bruus and Karsten Flensberg Many body quantum theory in condensed matter physics Reprint. Oxford [u.a.] Oxford Univ. Press 2007 XIX, 435 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts Vielkörperproblem - Kondensierte Materie - Quantenmechanisches System Vielkörperproblem (DE-588)4078900-7 gnd rswk-swf Vielteilchentheorie (DE-588)4331960-9 gnd rswk-swf Festkörperphysik (DE-588)4016921-2 gnd rswk-swf Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Festkörperphysik (DE-588)4016921-2 s Vielteilchentheorie (DE-588)4331960-9 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 Vielkörperproblem (DE-588)4078900-7 s Flensberg, Karsten Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015681612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bruus, Henrik Flensberg, Karsten Many-body quantum theory in condensed matter physics an introduction Vielkörperproblem - Kondensierte Materie - Quantenmechanisches System Vielkörperproblem (DE-588)4078900-7 gnd Vielteilchentheorie (DE-588)4331960-9 gnd Festkörperphysik (DE-588)4016921-2 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| subject_GND | (DE-588)4078900-7 (DE-588)4331960-9 (DE-588)4016921-2 (DE-588)4047984-5 (DE-588)4123623-3 |
| title | Many-body quantum theory in condensed matter physics an introduction |
| title_alt | Many body quantum theory in condensed matter physics |
| title_auth | Many-body quantum theory in condensed matter physics an introduction |
| title_exact_search | Many-body quantum theory in condensed matter physics an introduction |
| title_exact_search_txtP | Many-body quantum theory in condensed matter physics an introduction |
| title_full | Many-body quantum theory in condensed matter physics an introduction Henrik Bruus and Karsten Flensberg |
| title_fullStr | Many-body quantum theory in condensed matter physics an introduction Henrik Bruus and Karsten Flensberg |
| title_full_unstemmed | Many-body quantum theory in condensed matter physics an introduction Henrik Bruus and Karsten Flensberg |
| title_short | Many-body quantum theory in condensed matter physics |
| title_sort | many body quantum theory in condensed matter physics an introduction |
| title_sub | an introduction |
| topic | Vielkörperproblem - Kondensierte Materie - Quantenmechanisches System Vielkörperproblem (DE-588)4078900-7 gnd Vielteilchentheorie (DE-588)4331960-9 gnd Festkörperphysik (DE-588)4016921-2 gnd Quantenfeldtheorie (DE-588)4047984-5 gnd |
| topic_facet | Vielkörperproblem - Kondensierte Materie - Quantenmechanisches System Vielkörperproblem Vielteilchentheorie Festkörperphysik Quantenfeldtheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015681612&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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