Supersymmetry in disorder and chaos
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| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1999
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| Ausgabe: | 1. paperback ed. |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Efetov, Konstantin |d 1950-2021 |e Verfasser |0 (DE-588)143777173 |4 aut | |
| 245 | 1 | 0 | |a Supersymmetry in disorder and chaos |c Konstantin Efetov |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1999 | |
| 300 | |a XIII, 441 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Supersymétrie |2 ram | |
| 650 | 4 | |a Condensed matter | |
| 650 | 4 | |a Metals |x Surfaces | |
| 650 | 4 | |a Order-disorder in alloys | |
| 650 | 4 | |a Quantum chaos | |
| 650 | 4 | |a Semiconductors | |
| 650 | 4 | |a Supersymmetry | |
| 650 | 4 | |a Supersymmetry |x Industrial applications | |
| 650 | 0 | 7 | |a Ungeordnetes System |0 (DE-588)4124353-5 |2 gnd |9 rswk-swf |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-014584741 | |
Datensatz im Suchindex
| _version_ | 1819686125181075456 |
|---|---|
| adam_text | Contents
Preface
page
xi
Acknowledgments
xiii
1
Introduction
1
1.1
Historical remarks
1
1.2
What is this book about?
3
2
Supermathematics
б
2.1
What is supermathematics?
8
2.2 Grassmann
variables
9
2.3
Supervectors and
supermatrices
11
2.3.1
Definitions and basic properties
11
2.3.2
Supertrace
and superdeterminant
15
2.4
Integrals
17
2.4.1
Integrals over anticommuting variables
17
2.4.2
Superintegrals
19
2.5
Changing the variables
21
2.5.1
General formulae
21
2.5.2
Integral over supervector
23
2.5.3
Integral over supermatrix
25
2.5.4
Jacobian (Berezmian) and length in superspace
27
3
Diffusion modes
29
3.1
Quantum interference on defects
29
3.1.1
Localization
29
3.1.2
Multiple interference
32
3.1.3
Magnetic field effects
34
3.2
Choice of the model and correlation functions
35
3.3
Averaging over impurities: Classical formulae
40
3.4
Quantum corrections
44
4
Nonlinear supermatrix
σ
-model
50
4.1
Reduction to a regular model, mean field theory
50
4.1.1
Regular model with interaction
50
4.1.2
Mean field theory
53
4.2
Derivation of the
σ
-model
56
vi
Contents
4.2.1
Hubbard-Stratonovich
transformation
56
4.2.2
Saddle point
61
4.2.3
σ
-Model
63
4.3
Magnetic and spin-orbit interactions
66
4.3.1
Magnetic field
66
4.3.2
Magnetic impurities
67
4.3.3
Spin-orbit impurities
69
5
Perturbation theory and renormalization group
73
5.1
Perturbation theory
73
5.1.1
First quantum correction
73
5.1.2
Magnetic field and magnetic and spin-orbit impurities
76
5.2
Renormalization group in
2 +
e
dimensions
79
5.2.1
Renormalization group procedure
79
5.2.2
Gell-Mann-Low function and physical quantities
83
6
Energy level statistics
88
6.1
Random matrix theory
88
6.1.1
General formulation
88
6.1.2
Applications of
RMT
92
6.2
Zero-dimensional supermatrix
σ
-model
96
6.2.1
Diffusion in a limited volume
96
6.2.2
Correlation functions through definite integrals over
supermatrices
99
6.3
Reduction to integrals over eigenvalues
102
6.4
The level-level correlation function
109
6.5
Random matrix theory and zero-dimensional
σ
-model
114
7
Quantum size effects in small metal particles
119
7.1
Small metal particles
119
7.1.1
General properties
119
7.1.2
Gorkov and Eliashberg theory
122
7.2
Electric susceptibility
126
7.2.1
Reduction to the
σ
-model
126
7.2.2
Calculation of integrals over supermatrix
g
130
7.2.3
Possibility of experimental observation
135
7.3
Local density of states distribution function and NMR
138
7.3.1
NMR intensity line and the
σ
-model
138
7.3.2
Density of states distribution function
143
7.3.3
NMR line shape-comparison with experiments
148
8
Persistent currents in mesoscopic rings
152
8.1
Basic properties
152
8.2
Diffusion modes and persistent currents
157
8.2.1
Typical current
157
8.2.2
Canonical versus grand canonical
161
8.2.3
Average current
163
Contents
vii
8.3 Nonperturbative calculations
at arbitrary magnetic field
166
8.3.1
Integral over
supermatrices
166
8.3.2
Level-level correlation function and persistent current
170
8.4
Dynamic approach
174
8.4.1
Thermodynamics through a dynamic response
174
8.4.2
Calculation of current
178
8.4.3
Comparison with results of numerical simulations
182
8.5
Effects of spin-orbit interactions
184
9
Transport through raesoscopic devices
189
9.1
Universal conductance fluctuations
189
9.1.1
Diffusion modes and conductance fluctuations
189
9.1.2
Correlation function of conductances
193
9.2
Nonlinear
σ
-model for a system with leads
196
9.2.1 Landauer
approach
196
9.2.2
Elimination of the leads
199
9.2.3
σ
-Model for a system with leads
202
9.3
Semiclassical theory of transport
206
9.3.1
Addition of resistances
206
9.3.2
Weak localization effects
210
9.4
Conductance fluctuations in the semiclassical limit
212
9.4.1
Reduction of correlation functions of conductances to
integrals over
supermatrices
212
9.4.2
Temperature effects
215
9.5
Average conductance and variance in quantum limit
221
9.6
Conductance distribution function
224
9.6.1
The distribution function in terms of a definite integral
224
9.6.2
The limit
t ¿
<K t: Random phases of eigenstates and
independent fluctuations of amplitudes at different points
228
9.6.3
General form of the distribution function
232
9.7
Statistical theory of Coulomb blockade oscillations
234
9.7.1
Phenomenological approach
234
9.7.2
Distribution function of conductance peaks
237
9.7.3
Distribution function of wave functions at an arbitrary
magnetic field
240
10
Universal parametric correlations
246
10.1
Brownian motion model
246
10.1.1
Fokker-Planck equation for the Coulomb gas model
246
10.1.2
Brownian motion of a matrix
249
10.1.3
Relation between the Brownian motion and
Calogero-Sutherland models
251
10.2
Universalities in disordered and chaotic systems spectra
254
10.2.1
General formulae
254
10.2.2
Correlation function of density of states at different values
of external fields
257
10.2.3
Universal form of parametric correlations
258
viii Contents
10.2.4
Some other parametric correlations
263
10.3
Grand unification
266
10.3.1
Parametric correlations and one-dimensional
fermions
266
10.3.2
Continuous matrix model and one-dimensional fermionic
systems
268
10.3.3
Continuous matrix model and a supermatrix
σ
-model
270
10.3.4
Discussion of the connections
272
11
Localization in systems with one-dimensional geometry
274
11.1
One-dimensional
σ
-model
274
11.1.1
One-dimensional
σ
-model
for disorder problems
274
11.1.2
One-dimensional
σ
-model and some problems of quantum
chaos
278
11.2
Transfer matrix technique
280
11.2.1
General equations
280
11.2.2
Partial differential equations
284
11.3
Density-density correlator and dielectric permeability
287
11.3.1
High-frequency limit
287
11.3.2
Low-frequency limit
289
11.4
Inverse participation ratio in a finite sample
293
11.5
Conductance of a finite sample
297
11.6
Strong disorder
301
11.6.1
Fourier series for the density-density correlation function
301
11.6.2
Unitary ensemble: Integral equations in an explicit form
304
11.6.3
Low-frequency limit
305
11.6.4
Symplectic and orthogonal ensembles
309
11.7
Diamagnetism due to localization
311
11.7.1
Level crossing and difference between dynamic and
thermodynamic quantities: Basic equations
311
11.7.2
Diamagnetism from the one-dimensional
σ
-model
3
14
11.7.3
Possibility of experimental observation
315
12
Anderson metal-insulator transition
318
12.1
Description of phase transitions
318
12.1.1
Phenomenological approach
318
12.1.2
Phase transitions in spin models
322
12.2
Effective medium approximation
327
12.2.1
Perturbation theory: Need for partial summation
327
12.2.2
Principal approximation
331
12.3
Metal-insulator transition and functional order parameter
334
12.3.1
General properties of the main equation
334
12.3.2
Transition point and solutions
336
12.4
Correlation functions
341
12.4.1
General formulae
341
12.4.2
Insulator
343
12.4.3
Density-density correlation function in the metallic region
346
Contents ix
12.4.4
Correlation function of the density of states in the metallic
region
352
12.5
Interpretation of the results
355
12.5.1
Noncompactness: Formal reason for the unconventional
behavior
355
12.5.2
Physical picture: Quasi-localized states
359
12.5.3
Effective medium approximation and reality
362
12.6
Bethe lattice, highly conducting polymers, sparse matrices
365
12.6.1
Models on the Bethe lattice
365
12.6.2
Highly conducting polymers
366
12.6.3
Sparse random matrices
372
13
Disorder in two dimensions
376
13.1
Electron in a strong magnetic field
376
13.1.1
General remarks
376
13.1.2
Density of states
377
13.1.3
Integer quantum Hall effect
381
13.1.4
Hall insulator
384
13.1.5
Transition between Hall plateaus
386
13.2
Multifractality of eigenstates in 2D disordered metals
391
13.2.1
What is multifractality?
391
13.2.2
Reduced
σ
-model and its saddle points
393
13.2.3
Distribution function and coefficients of the inverse
participation ratio
396
14
Afterword
402
Appendix
1
Calculation of the Jacobian
404
Appendix
2
Magnetic field parametrization
408
Appendix
3
Density-density correlation function atk = 0
411
Appendix
4
Effective medium approximation as a saddle point
415
A4.1 Effective Lagrangian
415
A4.2 Saddle point
418
References
421
Author index
433
Subject index
438
|
| any_adam_object | 1 |
| author | Efetov, Konstantin 1950-2021 |
| author_GND | (DE-588)143777173 |
| author_facet | Efetov, Konstantin 1950-2021 |
| author_role | aut |
| author_sort | Efetov, Konstantin 1950-2021 |
| author_variant | k e ke |
| building | Verbundindex |
| bvnumber | BV021263523 |
| callnumber-first | Q - Science |
| callnumber-label | QC174 |
| callnumber-raw | QC174.17.S9 |
| callnumber-search | QC174.17.S9 |
| callnumber-sort | QC 3174.17 S9 |
| callnumber-subject | QC - Physics |
| classification_rvk | UO 1560 |
| classification_tum | PHY 623f PHY 026f PHY 012f |
| ctrlnum | (OCoLC)41925939 (DE-599)BVBBV021263523 |
| dewey-full | 530.413 539.725 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics 539 - Modern physics |
| dewey-raw | 530.413 539.725 |
| dewey-search | 530.413 539.725 |
| dewey-sort | 3530.413 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV021263523 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T19:11:34Z |
| institution | BVB |
| isbn | 0521663822 9780521663823 9780521470971 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014584741 |
| oclc_num | 41925939 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-83 |
| physical | XIII, 441 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Efetov, Konstantin 1950-2021 Supersymmetry in disorder and chaos Supersymétrie ram Condensed matter Metals Surfaces Order-disorder in alloys Quantum chaos Semiconductors Supersymmetry Supersymmetry Industrial applications Ungeordnetes System (DE-588)4124353-5 gnd Supersymmetrie (DE-588)4128574-8 gnd Vielteilchensystem (DE-588)4063491-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Festkörper (DE-588)4016918-2 gnd |
| subject_GND | (DE-588)4124353-5 (DE-588)4128574-8 (DE-588)4063491-7 (DE-588)4037952-8 (DE-588)4016918-2 |
| title | Supersymmetry in disorder and chaos |
| title_auth | Supersymmetry in disorder and chaos |
| title_exact_search | Supersymmetry in disorder and chaos |
| title_full | Supersymmetry in disorder and chaos Konstantin Efetov |
| title_fullStr | Supersymmetry in disorder and chaos Konstantin Efetov |
| title_full_unstemmed | Supersymmetry in disorder and chaos Konstantin Efetov |
| title_short | Supersymmetry in disorder and chaos |
| title_sort | supersymmetry in disorder and chaos |
| topic | Supersymétrie ram Condensed matter Metals Surfaces Order-disorder in alloys Quantum chaos Semiconductors Supersymmetry Supersymmetry Industrial applications Ungeordnetes System (DE-588)4124353-5 gnd Supersymmetrie (DE-588)4128574-8 gnd Vielteilchensystem (DE-588)4063491-7 gnd Mathematische Physik (DE-588)4037952-8 gnd Festkörper (DE-588)4016918-2 gnd |
| topic_facet | Supersymétrie Condensed matter Metals Surfaces Order-disorder in alloys Quantum chaos Semiconductors Supersymmetry Supersymmetry Industrial applications Ungeordnetes System Supersymmetrie Vielteilchensystem Mathematische Physik Festkörper |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014584741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT efetovkonstantin supersymmetryindisorderandchaos |