Nonequilibrium many-body theory of quantum systems: a modern introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XVII, 600 S. graph. Darst. |
| ISBN: | 9780521766173 |
Internformat
MARC
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| 100 | 1 | |a Stefanucci, Gianluca |d 1973- |e Verfasser |0 (DE-588)1033899038 |4 aut | |
| 245 | 1 | 0 | |a Nonequilibrium many-body theory of quantum systems |b a modern introduction |c Gianluca Stefanucci ; Robert van Leeuwen |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2013 | |
| 300 | |a XVII, 600 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Green's functions | |
| 650 | 4 | |a Many-body problem | |
| 650 | 4 | |a Quantum theory / Mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Quantentheorie | |
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| 689 | 0 | 0 | |a Vielteilchensystem |0 (DE-588)4063491-7 |D s |
| 689 | 0 | 1 | |a Nichtgleichgewichtsthermodynamik |0 (DE-588)4130850-5 |D s |
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| 700 | 1 | |a Leeuwen, Robert van |e Verfasser |0 (DE-588)1033899429 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025890518 | ||
Datensatz im Suchindex
| _version_ | 1804150203027030016 |
|---|---|
| adam_text | Contents
Preface
xi
List of abbreviations and acronyms
xv
Fundamental constants and basic relations
xvii
1
Second quantization
1
1.1
Quantum mechanics of one particle
Ì
1.2
Quantum mechanics of many particles
7
1.3
Quantum mechanics of many identical particles
10
1.4
Field operators
17
1.5
General basis states
22
1.6
Hamiltonian in second quantization
26
1.7
Density matrices and quantum averages
35
2
Getting familiar with second quantization: model Hamiltonians
39
2.1
Model Hamiltonians
39
2.2
Pariser-Parr-Pople model
41
2.3
Noninteracting models
45
2.3.1
Bloch theorem and band structure
46
2.3.2
Fano
model
54
2.4
Hubbard model
59
2.4.1
Particle-hole symmetry: application to
the Hubbard dimer
61
2.5 Heisenberg
model
64
2.6
BCS model and the exact Richardson solution
67
2.7 Holstein
model
71
2.7.1
Peierls instability
74
2.7.2
Lang-Firsov transformation: the heavy polaron
76
3
Time-dependent problems and equations of morion
81
3.1
Introduction
81
3.2
Evolution operator
82
3.3
Equations of motion for operators in the
Heisenberg
picture
86
vi
Contents
3.4
Continuity equation: paramagnetic and diamagnetic currents
89
3.5
Lorentz
Force
92
4
The contour idea
95
4.1
Time-dependent quantum averages
95
4.2
Time-dependent ensemble averages
100
4.3
minai
equilibrium and adiabatic switching
106
4.4
Equations of motion on the contour
ПО
4.5
Operator correlators on the contour
114
5
Many-particle Green s functions
125
5.1
Martin-Schwinger hierarchy
125
5.2
Truncation of the hierarchy
129
5.3
Exact solution of the hierarchy from Wick s theorem
135
5.4
Finite and zero-temperature formalism from the exact solution
140
5.5
Langreth rules
143
6
One-particle Green s function
153
6.1
What can we learn
from G1.
153
6.1.1
The inevitable emergence of memory
155
6.1.2
Matsubara Green s function and initial preparations
158
6.1.3
Lesser/greater Green s function: relaxation and quasi-particles
161
6.2
Noninteracting Green s function
168
6.2.1
Matsubara component
169
6.2.2
Lesser and greater components
171
6.2.3
All other components and a useful exercise
173
6.3
Interacting Green s function and
Lehmann
representation
178
6.3.1
Steady-states, persistent oscillations,
initial-state dependence
179
6.3.2
Fluctuation-dissipation theorem and other
exact properties
186
6.3.3
Spectral function and probability interpretation
190
6.3.4 Photoemission
experiments and interaction effects
194
6.4
Total energy from the Galitskii-Migdal formula
202
7
Mean field approximations
205
7.1
Introduction
205
7.2
Hartree
approximation
207
7.2.1
Hartree
equations
208
7.2.2
Electron gas
211
7.2.3
Quantum discharge of a capacitor
213
7.3
Hartree
-Fock approximation
224
7.3.1
Hartree-Fock equations
225
7.3.2
Coulombic electron gas and spin-polarized solutions
228
Contents
vii
8
Conserving approximations: two-particle Green s function
235
8.1
Introduction
235
8.2
Conditions on the approximate
Gì
237
8.3
Continuity equation
238
8.4
Momentum conservation law
240
8.5
Angular momentum conservation law
242
8.6
Energy conservation law
243
9
Conserving approximations: self-energy
249
9.1
Self-energy and Dyson equations I
249
9.2
Conditions on the approximate
Σ
253
9.3
Φ
functional
255
9.4
Kadanoff-Baym equations
260
9.5
Fluctuation-dissipation theorem for the self-energy
264
9.6
Recovering equilibrium from the Kadanoff-Baym equations
267
9.7
Formal solution of the Kadanoff-Baym equations
270
10
MBPT for the Green s function
275
10.1
Getting started with Feynman diagrams
275
10.2
Loop rule
279
10.3
Cancellation of disconnected diagrams
280
10.4
Summing only the topologically inequivalent diagrams
283
10.5
Self-energy and Dyson equations II
285
10.6
G-skeleton diagrams
287
10.7
H^-skeleton diagrams
289
10.8
Summary and Feynman rules
292
11
MBPT and variational principles for the grand potential
295
11.1
Linked cluster theorem
295
11.2
Summing only the topologically inequivalent diagrams
299
11.3
How to construct the
Φ
functional
300
11.4
Dressed expansion of the grand potential
307
П.5
Luttinger-Ward and Klein functionals
309
11.6
Luttinger-Ward theorem
312
11.7
Relation between the reducible polarizability and the
Φ
functional
314
П.8
Φ
functional
318
11.9
Screened functionals
320
12
MBPT for the two-particle Green s function
323
12.1
Diagrams for G2 and loop rule
323
12.2
Bethe-Salpeter equation
326
123
Excitons
331
12.4
Diagrammatic proof of
К
—
±6E/őG
337
12.5
Vertex function and
Hedin
equations
339
viii Contents
13
Applications
of MBPT to equilibrium problems
347
13.1
Lifetimes and quasi-particles
347
13.2
Fluctuation-dissipation theorem for
Ρ
and
W
352
13.3
Correlations in the second-Born approximation
354
13.3.1
Polarization effects
357
13.4
Ground-state energy and correlation energy
362
13.5
GW correlation energy of a Coulombic electron gas
367
13.6
Т
-matrix approximation
373
13.6.1
Formation of a Cooper pair
378
14
Linear response theory: preliminaries
385
14.1
Introduction
385
14.2
Shortcomings of the linear response theory
386
14.2.1
Discrete-discrete coupling
387
14.2.2
Discrete-continuum coupling
390
14.2.3
Continuum-continuum coupling
396
14.3
Fermi golden rule
401
14.4
Kubo
formula
404
15
Linear response theory: many-body formulation
407
15.1
Current and density response function
407
15.2 Lehmann
representation
411
15.2.1
Analytic structure
414
15.2.2
The /-sum rule
416
15.2.3
Noninteracting
fermions
418
15.3
Bethe-Salpeter equation from the variation of a conserving
G
420
15.4
Ward identity and the /-sum rule
424
15.5
Time-dependent screening in an electron gas
427
15.5.1
Noninteracting density response function
428
15.5.2
RPA
density response function
431
15.5.3
Sudden creation of a localized hole
437
15.5.4
Spectral properties in the GoWo approximation
441
16
Applications of MBPT to nonequilibrium problems
455
16.1
Kadanoff-Baym equations for open systems
457
16.2
Time-dependent quantum transport: an exact solution
460
16.2.1 Landauer-Büttiker
formula
467
16.3
Implementation of the KadanofF-Baym equations
471
16.3.1
Time-stepping technique
472
16.3.2
Second-Born and GW self-energies
473
16.4
Initial-state and history dependence
476
16.5
Charge conservation
482
16.6
Time-dependent GW approximation in open systems
484
16.6.1
Keldysh Green s functions in the double-time plane
485
16.6.2
Time-dependent current and spectral function
486
Contents ix
16.6.3
Screened interaction and physical interpretation
490
16.7
Inbedding
technique: how to explore the reservoirs
492
16.8
Response functions from time-propagation
496
Appendices
A From the
Л/
roots of
1
to the Dirac ¿-function
503
В
Graphical approach to
permanents
and determinants
506
С
Density matrices and probability interpretation
517
D
Thermodynamics and statistical mechanics
523
E
Green s functions and lattice symmetry
529
F
Asymptotic expansions
534
G
Wick s theorem for general initial states
537
H BBGKY
hierarchy
552
I From ¿-like peaks to continuous spectral functions
555
J Virial
theorem for conserving approximations
559
К
Momentum distribution and sharpness of the Fermi surface
563
L
Hedin
equations from a generating functional
566
M
Lippmann-Schwinger
equation and cross-section
572
N
Why the name Random Phase Approximation?
577
O Kramers-Kronig
relations
582
P
Algorithm for solving the Kadanoff-Baym equations
584
References
587
Index
593
The Green s function method is one of the most
powerful and versatile formalisms in physics, and
its nonequilibrium version has proved invaluable in
many research fields. This book provides a unique,
self-contained introduction to nonequilibrium
many-body theory.
Starting with basic quantum mechanics, the authors
introduce the equilibrium and nonequilibrium Green s
function formalisms within a unified framework
called the contour formalism. The physical content of
the contour Green s functions and the diagrammatic
expansions are explained with a focus on the
time-dependent aspect. Every result is derived step-
by-step, critically discussed, and then applied to
different physical systems, ranging from molecules
and nanostructures to metals and insulators. With
an abundance of illustrative examples, this accessible
book is ideal for graduate students and researchers
who are interested in excited state properties of
matter and nonequilibrium physics.
Gianluca Stefanucci
is a Researcher at the
Physics Department of
the University of Rome
Tor
Vergata,
Italy. His
current research interests
are in quantum transport
through nanostructures
and nonequilibrium open
systems.
Robert van
Leeuwen
is
Professor of Physics at the
University of
Jyväskylä in
Finland. His main areas
of research are time-
dependent quantum
systems, many-body theory,
and quantum transport
through nanostructures.
|
| any_adam_object | 1 |
| author | Stefanucci, Gianluca 1973- Leeuwen, Robert van |
| author_GND | (DE-588)1033899038 (DE-588)1033899429 |
| author_facet | Stefanucci, Gianluca 1973- Leeuwen, Robert van |
| author_role | aut aut |
| author_sort | Stefanucci, Gianluca 1973- |
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| bvnumber | BV040911191 |
| classification_rvk | UL 1000 UL 3000 |
| classification_tum | PHY 062f PHY 026f |
| ctrlnum | (OCoLC)835689397 (DE-599)BVBBV040911191 |
| discipline | Physik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV040911191 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:35:06Z |
| institution | BVB |
| isbn | 9780521766173 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025890518 |
| oclc_num | 835689397 |
| open_access_boolean | |
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| owner_facet | DE-19 DE-BY-UBM DE-384 DE-703 DE-11 DE-355 DE-BY-UBR DE-29T DE-20 DE-91G DE-BY-TUM |
| physical | XVII, 600 S. graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Stefanucci, Gianluca 1973- Verfasser (DE-588)1033899038 aut Nonequilibrium many-body theory of quantum systems a modern introduction Gianluca Stefanucci ; Robert van Leeuwen 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2013 XVII, 600 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Green's functions Many-body problem Quantum theory / Mathematics Mathematik Quantentheorie Vielteilchensystem (DE-588)4063491-7 gnd rswk-swf Green-Funktion (DE-588)4158123-4 gnd rswk-swf Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd rswk-swf Vielteilchensystem (DE-588)4063491-7 s Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 s Green-Funktion (DE-588)4158123-4 s DE-604 Leeuwen, Robert van Verfasser (DE-588)1033899429 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025890518&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025890518&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Stefanucci, Gianluca 1973- Leeuwen, Robert van Nonequilibrium many-body theory of quantum systems a modern introduction Green's functions Many-body problem Quantum theory / Mathematics Mathematik Quantentheorie Vielteilchensystem (DE-588)4063491-7 gnd Green-Funktion (DE-588)4158123-4 gnd Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd |
| subject_GND | (DE-588)4063491-7 (DE-588)4158123-4 (DE-588)4130850-5 |
| title | Nonequilibrium many-body theory of quantum systems a modern introduction |
| title_auth | Nonequilibrium many-body theory of quantum systems a modern introduction |
| title_exact_search | Nonequilibrium many-body theory of quantum systems a modern introduction |
| title_full | Nonequilibrium many-body theory of quantum systems a modern introduction Gianluca Stefanucci ; Robert van Leeuwen |
| title_fullStr | Nonequilibrium many-body theory of quantum systems a modern introduction Gianluca Stefanucci ; Robert van Leeuwen |
| title_full_unstemmed | Nonequilibrium many-body theory of quantum systems a modern introduction Gianluca Stefanucci ; Robert van Leeuwen |
| title_short | Nonequilibrium many-body theory of quantum systems |
| title_sort | nonequilibrium many body theory of quantum systems a modern introduction |
| title_sub | a modern introduction |
| topic | Green's functions Many-body problem Quantum theory / Mathematics Mathematik Quantentheorie Vielteilchensystem (DE-588)4063491-7 gnd Green-Funktion (DE-588)4158123-4 gnd Nichtgleichgewichtsthermodynamik (DE-588)4130850-5 gnd |
| topic_facet | Green's functions Many-body problem Quantum theory / Mathematics Mathematik Quantentheorie Vielteilchensystem Green-Funktion Nichtgleichgewichtsthermodynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025890518&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025890518&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT stefanuccigianluca nonequilibriummanybodytheoryofquantumsystemsamodernintroduction AT leeuwenrobertvan nonequilibriummanybodytheoryofquantumsystemsamodernintroduction |