Quantum signatures of chaos:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Edition: | 3., rev. and enl. ed. |
| Series: | Springer series in synergetics
54 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXIII, 573 S. graph. Darst. |
| ISBN: | 9783642054273 9783642054280 9783642263309 |
Staff View
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Record in the Search Index
| _version_ | 1805094361127452672 |
|---|---|
| adam_text |
REFERENCES 58 CONTENTS 1 INTRODUCTION 1 REFERENCES 13 2 TIME REVERSAL
AND UNITARY SYMMETRIES 15 2. 1 AUTONOMOUS CLASSICAL FLOWS 15 2.2
SPINLESS QUANTA 16 2.3 SPIN-1/2 QUANTA 17 2.4 HAMILTONIANS WITHOUT T
INVARIANCE 19 2.5 T INVARIANT HAMILTONIANS, T 1 = 1 21 2.6 KRAMERS'
DEGENERACY 22 2.7 KRAMERS' DEGENERACY AND GEOMETRIC SYMMETRIES 22 2.8
KRAMERS' DEGENERACY WITHOUT GEOMETRIC SYMMETRIES 25 2.9 NONCONVENTIONAL
TIME REVERSAL 27 2.10 STROBOSCOPIE MAPS FOR PERIODICALLY DRIVEN SYSTEMS
29 2.11 TIME REVERSAL FOR MAPS 31 2.12 CANONICAL TRANSFORMATIONS FOR
FLOQUET OPERATORS 33 2.13 BEYOND DYSON'S THREEFOLD WAY 36 2.13.1
NORMAL-SUPERCONDUCTING HYBRID STRUCTURES 38 2.13.2 SYSTEMS WITH CHIRAL
SYMMETRY 43 2.14 PROBLEMS 44 REFERENCES 45 3 LEVEL REPULSION 47 3.1
PRELIMINARIES 47 3.2 SYMMETRIC VERSUS NONSYMMETRIC H OR F 48 3.3
KRAMERS' DEGENERACY 50 3.4 UNIVERSALITY CLASSES OF LEVEL REPULSION 52
3.5 NONSTANDARD SYMMETRY CLASSES 54 3.6 EXPERIMENTAL OBSERVATION OF
LEVEL REPULSION 56 3.7 PROBLEMS 57 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1002586569 DIGITALISIERT DURCH CONTENTS RANDOM-MATRIX
THEORY 61 4. 1 PRELIMINARIES 61 4.2 GAUSSIAN ENSEMBLES OF HERMITIAN
MATRICES 62 4.3 EIGENVALUE DISTRIBUTIONS FOR DYSON'S ENSEMBLES 66 4.4
EIGENVALUE DISTRIBUTIONS FOR NONSTANDARD SYMMETRY CLASSES . 68 4.5
LEVEL SPACING DISTRIBUTIONS 69 4.6 INVARIANCE OF THE INTEGRATION MEASURE
71 4.7 AVERAGE LEVEL DENSITY 73 4.8 UNFOLDING SPECTRA 74 4.9 EIGENVECTOR
DISTRIBUTIONS 76 4.9.1 SINGLE-VECTOR DENSITY 76 4.9.2 JOINT DENSITY OF
EIGENVECTORS 80 4.10 ERGODICITY OF THE LEVEL DENSITY 81 4.11 DYSON'S
CIRCULAR ENSEMBLES 84 4.12 ASYMPTOTIC LEVEL SPACING DISTRIBUTIONS 86
4.13 DETERMINANTS AS GAUSSIAN GRASSMANN INTEGRALS 96 4.14 TWO-POINT
CORRELATIONS OF THE LEVEL DENSITY 101 4.14.1 TWO-POINT CORRELATOR AND
FORM FACTOR 101 4.14.2 FORM FACTOR FOR THE POISSONIAN ENSEMBLE 103
4.14.3 FORM FACTOR FOR THE CUE 103 4.14.4 FORM FACTOR FOR THE COE 106
4.14.5 FORM FACTOR FOR THE CSE 110 4.15 NEWTON'S RELATIONS 112 4.15.1
TRACES VERSUS SECULAR COEFFICIENTS 112 4.15.2 SOLVING NEWTON'S RELATIONS
115 4.16 SELFINVERSIVENESS AND RIEMANN-SIEGEL LOOKALIKE 117 4.17 HIGHER
CORRELATIONS OF THE LEVEL DENSITY 118 4.17.1 CORRELATION AND CUMULANT
FUNCTIONS 118 4.17.2 ERGODICITY OF THE TWO-POINT CORRELATOR 121 4.17.3
ERGODICITY OF THE FORM FACTOR 124 4.17.4 JOINT DENSITY OF TRACES OF
LARGE CUE MATRICES 127 4.1 CONTENTS 5.8 LEVEL DENSITY FLUCTUATIONS FOR
INTEGRABLE SYSTEMS 158 5.9 EXPONENTIAL SPACING DISTRIBUTION FOR
INTEGRABLE SYSTEMS 165 5.10 EQUIVALENCE OF DIFFERENT UNFOLDINGS 166 5.11
PROBLEMS 167 REFERENCES 168 LEVEL DYNAMICS 169 6.1 PRELIMINARIES 169 6.2
FICTITIOUS PARTICLES (PECHUKAS-YUKAWA GAS) 170 6.3 CONSERVATION LAWS 177
6.4 INTERMULTIPLET CROSSINGS 180 6.5 LEVEL DYNAMICS FOR CLASSICALLY
INTEGRABLE DYNAMICS 181 6.6 TWO-BODY COLLISIONS 187 6.7 ERGODICITY OF
LEVEL DYNAMICS AND UNIVERSALITY OF SPECTRAL FLUCTUATIONS 188 6.7.1
ERGODICITY 188 6.7.2 COLLISION TIME 189 6.7.3 UNIVERSALITY 190 6.8
EQUILIBRIUM STATISTICS 192 6.9 RANDOM-MATRIX THEORY AS EQUILIBRIUM
STATISTICAL MECHANICS. 195 6.9.1 GENERAL STRATEGY 195 6.9.2 A TYPICAL
COORDINATE INTEGRAL 199 6.9.3 INFLUENCE OF A TYPICAL CONSTANT OF THE
MOTION 205 6.9.4 THE GENERAL COORDINATE INTEGRAL 206 6.9.5 CONCLUDING
REMARKS 208 6.10 DYNAMICS OF RESCALED ENERGY LEVELS 209 6.11 LEVEL
CURVATURE STATISTICS 212 6.12 LEVEL VELOCITY STATISTICS 221 6.13 DYSON'S
BROWNIAN-MOTION MODEL 224 6.14 LOCAL AND GLOBAL EQUILIBRIUM IN SPECTRA
234 6.15 PROBLEMS 242 REFERENCES 244 QUANTUM LOCALIZATION 247 7.1
PRELIMINARIES 247 7.2 LOCALIZATION IN ANDERSON'S HOPPING MODEL 248 7.3
THE KICKED ROTATOR AS A VARIANT OF ANDERSON'S MODEL 251 7. CX CONTENTS 8
DISSIPATIVE SYSTEMS 279 8. 1 PRELIMINARIES 279 8.2 HAMILTONIAN
EMBEDDINGS 279 8.3 TIME-SCALE SEPARATION FOR PROBABILITIES AND
COHERENCES 285 8.4 DISSIPATIVE DEATH OF QUANTUM RECURRENCES 288 8.5
COMPLEX ENERGIES AND QUASI-ENERGIES 296 8.6 DIFFERENT DEGREES OF LEVEL
REPULSION FOR REGULAR AND CHAOTIC MOTION 299 8.7 POISSONIAN RANDOM
PROCESS IN THE PLANE 302 8.8 GINIBRE'S ENSEMBLE OF RANDOM MATRICES 303
8.8.1 NORMALIZING THE JOINT DENSITY 304 8.8.2 THE DENSITY OF EIGENVALUES
306 8.8.3 THE REDUCED JOINT DENSITIES 308 8.8.4 THE SPACING DISTRIBUTION
309 8.9 GENERAL PROPERTIES OF GENERATORS 314 8.10 UNIVERSALITY OF CUBIC
LEVEL REPULSION 319 8.10.1 ANTIUNITARY SYMMETRIES 319 8.10.2
MICROREVERSIBILITY 321 8.11 DISSIPATION OF QUANTUM LOCALIZATION 326
8.11.1 ZASLAVSKY'S MAP 326 8.11.2 DAMPED ROTATOR 329 8.11.3 DESTRUCTION
OF LOCALIZATION 332 8.12 PROBLEMS 335 REFERENCES 338 9 CLASSICAL
HAMILTONIAN CHAOS 341 9.1 PRELIMINARIES 341 9.2 PHASE SPACE, HAMILTON'S
EQUATIONS AND ALL THAT 341 9.3 ACTION AS A GENERATING FUNCTION 343 9.4
LINEARIZED FLOW AND ITS JACOBIAN MATRIX 344 9.5 LIOUVILLE PICTURE 346
9.6 SYMPLECTIC STRUCTURE 347 9.7 LYAPUNOV EXPONENTS 348 9.8 STRETCHING
FACTORS AND LOCAL STRETCHING RATES 350 9. CONTENTS 9.15.2 QUANTITATIVE
DISCUSSION OF 2-ENCOUNTERS 366 9.16 /-ENCOUNTERS AND ORBIT BUNCHES 373
9.17 DENSITIES OF ARBITRARY ENCOUNTER SETS 379 9.18 PROBLEMS 380
REFERENCES 381 10 SEMICLASSICAL ROLES FOR CLASSICAL ORBITS 383 10.1
PRELIMINARIES 383 10.2 VAN VIECK PROPAGATOR 383 10.2.1 MAPS 384 10.2.2
FLOWS 390 10.3 GUTZWILLER'S TRACE FORMULA 393 10.3.1 MAPS 394 10.3.2
FLOWS 398 10.3.3 WEYL'S LAW 404 10.3.4 LIMITS OF VALIDITY AND OUTLOOK
405 10.4 LAGRANGIAN MANIFOLDS AND MASLOV THEORY 407 10.4.1 LAGRANGIAN
MANIFOLDS 407 10.4.2 ELEMENTS OF MASLOV THEORY 414 10.4.3 MASLOV INDICES
AS WINDING NUMBERS 418 10.5 RIEMANN-SIEGEL LOOK-ALIKE 422 10.6 SPECTRAL
TWO-POINT CORRELATOR 428 10.6.1 REAL AND COMPLEX CORRELATOR 428 10.6.2
LOCAL ENERGY AVERAGE 429 10.6.3 GENERATING FUNCTION 432 10.6.4
PERIODIC-ORBIT REPRESENTATION 433 10.7 DIAGONAL APPROXIMATION 437 10.7.1
UNITARY CLASS 437 10.7.2 ORTHOGONAL CLASS 439 10.8 OFF-DIAGONAL
CONTRIBUTIONS, UNITARY SYMMETRY CLASS 439 10.8.1 STRUCTURES OF
PSEUDO-ORBIT QUADRUPLETS 441 10.8.2 DIAGRAMMATIC RULES 444 10.8.3
EXAMPLE OF STRUCTURE CONTRIBUTIONS: A SINGLE 2-ENCOUNTER 446 10.8.4
CANCELLATION OF ALL ENCOUNTER CONTRIBUTIONS FOR THE UNITARY CLASS 447
10.9 SEMICLASSICAL CONSTRUCTION OF A SIGMA MODEL, UNITAR CONTENTS 10.10
SEMICLASSICAL CONSTRUCTION OF A SIGMA MODEL, ORTHOGONAL SYMMETRY CLASS
461 10.10.1 STRUCTURES 461 10.10.2 LEADING-ORDER CONTRIBUTIONS 462
10.10.3 SYMBOLS FOR PORTS AND CONTRACTION LINES FOR LINKS . 464
10.10.4 GAUSS AND WICK 465 10.10.5 SIGNS 466 10.10.6 PROOF OF
CONTRACTION RULES, ORTHOGONAL CASE 468 10.10.7 SIGMA MODEL 470 10.11
OUTLOOK 471 10.12 MIXED PHASE SPACE 472 10.13 PROBLEMS 475 REFERENCES
.477 11 SUPERANALYSIS FOR RANDOM-MATRIX THEORY 481 11.1 PRELIMINARIES
481 11.2 SEMICIRCLE LAW FOR THE GAUSSIAN UNITARY ENSEMBLE 482 11.2.1 THE
GREEN FUNCTION AND ITS AVERAGE 482 11.2.2 THE GUE AVERAGE 484 11.2.3
DOING THE SUPERINTEGRAL 484 11.2.4 TWO REMAINING SADDLE-POINT INTEGRALS
487 11.3 SUPERALGEBRA 490 11.3.1 MOTIVATION AND GENERATORS OF GRASSMANN
ALGEBRAS 490 11.3.2 SUPERVECTORS, SUPERMATRICES 491 11.3.3
SUPERDETERMINANTS 493 11.3.4 COMPLEX SCALAR PRODUCT, HERMITIAN AND
UNITARY SUPERMATRICES 495 11.3.5 DIAGONALIZING SUPERMATRICES 497 11.4
SUPERINTEGRALS 498 11.4.1 SOME BOOKKEEPING FOR ORDINARY GAUSSIAN
INTEGRALS 498 11.4.2 RECALLING GRASSMANN INTEGRALS 499 11.4.3 GAUSSIAN
SUPERINTEGRALS 501 11.4.4 SOME PROPERTIES OF GENERAL SUPERINTEGRALS 502
11.4.5 INTEGRALS OVER SUPERMATRICES, PARISI-SOURLAS-EFETOV-WEGNER
THEOREM 504 11. CONTENTS XXIUE 11.6.8 HIGH-ENERGY ASYMPTOTICS 539 11.7
UNIVERSALITY OF SPECTRAL FLUCTUATIONS: NON-GAUSSIAN ENSEMBLES 541 11.7.1
DELTA FUNCTIONS OF GRASSMANN VARIABLES 542 11.7.2 GENERATING FUNCTION
543 11.8 UNIVERSAL SPECTRAL FLUCTUATIONS OF SPARSE MATRICES 546 11.9
THICK WIRES, BANDED RANDOM MATRICES, ONE-DIMENSIONAL SIGMA MODEL 547
11.9.1 BANDED MATRICES MODELLING THICK WIRES 547 11.9.2 INVERSE
PARTICIPATION RATIO AND LOCALIZATION LENGTH . 549 11.9.3
ONE-DIMENSIONAL NONLINEAR SIGMA MODEL 550 11.9.4 IMPLEMENTING THE
ONE-DIMENSIONAL SIGMA MODEL 555 11.10 PROBLEMS 564 REFERENCES 566 INDEX
569 |
| any_adam_object | 1 |
| author | Haake, Fritz 1941-2019 |
| author_GND | (DE-588)1196383804 |
| author_facet | Haake, Fritz 1941-2019 |
| author_role | aut |
| author_sort | Haake, Fritz 1941-2019 |
| author_variant | f h fh |
| building | Verbundindex |
| bvnumber | BV036571458 |
| classification_rvk | UG 3900 UK 7600 |
| classification_tum | PHY 066f |
| ctrlnum | (OCoLC)637037356 (DE-599)DNB1002586569 |
| dewey-full | 530.12 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
| dewey-search | 530.12 |
| dewey-sort | 3530.12 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 3., rev. and enl. ed. |
| format | Book |
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| id | DE-604.BV036571458 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T10:42:10Z |
| institution | BVB |
| isbn | 9783642054273 9783642054280 9783642263309 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020492565 |
| oclc_num | 637037356 |
| open_access_boolean | |
| owner | DE-634 DE-19 DE-BY-UBM DE-83 DE-91G DE-BY-TUM DE-703 DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-634 DE-19 DE-BY-UBM DE-83 DE-91G DE-BY-TUM DE-703 DE-355 DE-BY-UBR DE-11 |
| physical | XXIII, 573 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in synergetics |
| series2 | Springer series in synergetics Springer complexity |
| spelling | Haake, Fritz 1941-2019 Verfasser (DE-588)1196383804 aut Quantum signatures of chaos Fritz Haake 3., rev. and enl. ed. Berlin [u.a.] Springer 2010 XXIII, 573 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in synergetics 54 Springer complexity Hier auch später erschienene, unveränderte Nachdrucke Chaostheorie (DE-588)4009754-7 gnd rswk-swf Quantenchaos (DE-588)4130849-9 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenchaos (DE-588)4130849-9 s DE-604 Quantenmechanik (DE-588)4047989-4 s Quantentheorie (DE-588)4047992-4 s Chaostheorie (DE-588)4009754-7 s 1\p DE-604 Springer series in synergetics 54 (DE-604)BV000005271 54 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3478411&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020492565&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Haake, Fritz 1941-2019 Quantum signatures of chaos Springer series in synergetics Chaostheorie (DE-588)4009754-7 gnd Quantenchaos (DE-588)4130849-9 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4130849-9 (DE-588)4047992-4 (DE-588)4047989-4 |
| title | Quantum signatures of chaos |
| title_auth | Quantum signatures of chaos |
| title_exact_search | Quantum signatures of chaos |
| title_full | Quantum signatures of chaos Fritz Haake |
| title_fullStr | Quantum signatures of chaos Fritz Haake |
| title_full_unstemmed | Quantum signatures of chaos Fritz Haake |
| title_short | Quantum signatures of chaos |
| title_sort | quantum signatures of chaos |
| topic | Chaostheorie (DE-588)4009754-7 gnd Quantenchaos (DE-588)4130849-9 gnd Quantentheorie (DE-588)4047992-4 gnd Quantenmechanik (DE-588)4047989-4 gnd |
| topic_facet | Chaostheorie Quantenchaos Quantentheorie Quantenmechanik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3478411&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020492565&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005271 |
| work_keys_str_mv | AT haakefritz quantumsignaturesofchaos |