Chaos and quantum chaos: proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Tagungsbericht Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest
Springer
1992
|
| Schriftenreihe: | Lecture notes in physics
411 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIV, 330 S. Ill., graph. Darst. |
| ISBN: | 3540562532 0387562532 |
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| 245 | 1 | 0 | |a Chaos and quantum chaos |b proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 |c W. Dieter Heiss (ed.) |
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Datensatz im Suchindex
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CONTENTS
THE PROBLEM OF QUANTUM CHAOS
BORIS V CHIRIKOV
1
1. INTRODUCTION: THE THEORY OF DYNAMICAL SYSTEMS
AND STATISTICAL PHYSICS 1
2. ASYMPTOTIC STATISTICAL PROPERTIES OF CLASSICAL DYNAMICAL
CHAOS 9
3. THE CORRESPONDENCE PRINCIPLE AND QUANTUM CHAOS 17
4. THE UNCERTAINTY PRINCIPLE AND THE TIME SCALES OF QUANTUM
DYNAMICS 20
5. FINITE-TIME STATISTICAL RELAXATION IN DISCRETE SPECTRUM
26
6. THE QUANTUM STEADY STATE 32
7. ASYMPTOTIC STATISTICAL PROPERTIES OF QUANTUM CHAOS 40
8. CONCLUSION: THE QUANTUM CHAOS AND TRADITIONAL STATISTICAL
MECHANICS 49
SEMI-CLASSICAL QUANTIZATION OF CHAOTIC BILLIARDS
UZY SMILANSKY 57
I INTRODUCTION 58
II CLASSICAL BILLIARDS 52
M QUANTIZATION - THE SEMI-QUANTA! SECULAR EQUATION 67
M.A QUANTIZATION OF CONVEX BILLIARDS 68
UL.B QUANTIZATION OF BILLIARDS WITH ARBITRARY SHAPES 70
M.C PROPERTIES OF THE SEMI.QUANTAL SECULAR EQUATION 75
IV THE SEMI-CLASSICAL SECULAR FUNCTION 80
V SPECTRAL DENSITIES 90
V.A THE AVERAGED SPECTRAL DENSITY 91
V.B THE GUTZWILLER TRACE FORMULAE FOR THE SPECTRAL 95
DENSITY
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/930082362
X
VI SPECTRAL CORRELATIONS
VI.A S MATRIX SPECTRAL CORRELATIONS 100
VI.B ENERGY SPECTRAL CORRELATIONS 104
VI.C COMPOSITE BILLIARDS 106
VII CONCLUSIONS 112
APPENDIX A US
STOCHASTIC SCATTERING THEORY OR RANDOMRMATRIX MODELS FOR
FLUCTUATIONS IN MICROSCOPIC AND MESOSCOPIC SYSTEMS
HANS A WEIDENMIAUER 121
1. MOTIVATION: THE PHENOMENA 122
1.1 MICROWAVE SCATTERING IN CAVITIES 124
1.2 COMPOUND-NUCLEUS SCATTERING IN THE DOMAINS OF
ISOLATED AND OF OVERLAPPING RESONANCES 126
1.3 CHAOTIC MOTION IN MOLECULES 128
1.4 PASSAGE OF LIGHT THROUGH A MEDIUM WITH A SPATIALLY
RANDOMLY VARYING INDEX OF REFRACTION 130
1.5 UNIVERSAL CONDUCTANCE FLUCTUATIONS 130
2. STOCHASTIC MODELLING 133
2.1 CHAOTIC AND COMPOUND-NUCLEUS SCATTERING 134
2.2 CONDUCTANCE FLUCTUATIONS 135
3. METHODS OF AVERAGING 137
3.1 MONTE-CARLO SIMULATION 137
3.2 DISORDER PERTURBATION THEORY 138
3.3 THE GENERATING FUNCTIONAL 139
4. CHAOTIC SCATTERING AND COMPOUND-NUCLEUS REACTIONS 141
5. UNIVERSAL CONDUCTANCE FLUCTUATIONS 151
6. PERSISTENT CURRENTS IN MESOSCOPIC RINGS 159
7. CONCLUSIONS 164
XI
ATOMIC AND MOLECULAR PHYSICS EXPERIMENTS IN QUANTUM
CHAOLOGY
PETER M KOCH 167
1. INTRODUCTION 168
1.1 THE DIAMAGNETIC KEPLER PROBLEM 170
1.2 SPECTROSCOPY OF HIGHLY EXCITED POLYATOMIC
MOLECULES 171
1.3 THE HELIUM ATOM 172
1.4 SWIFT IONS TRAVERSING FOILS 173
1.5 WHAT THIS PAPER COVERS AND DOES NOT COVER 174
2. APPARATUS AND EXPERIMENTAL METHOD 176
2.1 APPARATUS 176
2.2 EXPERIMENTAL METHODS 179
3. THE HAMILTONIAN AND SCALED VARIABLES 182
4. REGIMES OF BEHAVIOR 187
4.1 "IONIZATION" CURVES 187
5. STATIC FIELD IONIZATION 190
6. REGIME-I: THE DYNAMIC TUNNELING REGIME 191
7. REGIME-II: THE LOW FREQUENCY REGIME 194
8. REGIME-M : THE SEMI CLASSICAL REGIME 196
8.1 CLASSICAL KEPLER MAPS FOR ID MOTION 199
9. REGIME-IV: THE TRANSITION REGIME 203
9.1 NONCLASSICAL LOCAL STABILITY AND "SCARS" 206
10. REGIME-V: THE HIGH FREQUENCY REGIME 212
11. CONCLUSIONS 215
XII
TOPICS IN QUANTUM CHAOS
R E PRANGE 225
L.
INTRODUCTION 225
A. PHILOSOPHY 225
B. TIME SCALES 227
C. THE QUASICLASSICAL APPROXIMATION 228
D. PSEUDORANDOM MATRIX THEORY 229
E. TYPES OF CHAOTIC SYSTEMS 230
F. SUMMARY AND OUTLINE 232
N.
QUANTUM LONGTIME BEHAVIOR AND LOCALIZATION 233
A. THE KICKED ROTOR 233
B. TUNNELING AND KAM TORII 234
C. DYNAMIC LOCALIZATION 237
D. CONNECTION OF ANDERSON LOCALIZATION TO .QUANTUM CHAOS 241
E. PSEUDORANDOMNESS OF T
M 242
F. AN ASIDE ON LIOUVILLE NUMBERS 242
G. COMPARISON OF PSEUDORANDOM AND TRULY RANDOM
CASES 243
H. NUMERICAL SOLUTIONS 243
I. RELATIONSHIP OF THE LOCALIZATION LENGTH TO CLASSICAL
DIFFUSION 244
M. TRANSITIONS TO CHAOS 244
A. INTRODUCTION 244
B. THE LOGISTICS MAP 244
C. PERIOD DOUBLING SEQUENCE 246
D. HAMILTONIAN MAPS 252
E. LAST KAM TORUS 252
F. OTHER RELEVANT VARIABLES 254
G. PLANCK'S CONSTANT AS A RELEVANT VARIABLE 254
XIII
H. CONSEQUENCES OF SCALING 256
I. TUNNELLING THROUGH KAM BARRIERS 258
IV. VALIDITY OF THE SEMIDASSICAL APPROXIMATION IN QUANTUM
CHAOS 258
A. INTRODUCTION 258
B. QUANTUM MAPS 260
C. PERIODIC POINT EXPANSIONS 262
D. PROPAGATION OF GEOMETRY 263
E. VALIDITY OF THE ASSUMPTION OF PERIODIC POINT
DOMINANCE 265
F. GENERIC CHAOS 268
G. BREAKDOWN OF THE SEMIDASSICAL APPROXIMATION 269
H. CONDUSIONS AND ACKNOWLEDGEMENTS 270
DYNAMIC LOCALIZATION IN OPEN QUANTUM SYSTEMS
ROBERT GRAHAM 273
1. INTRODUCTION 273
2. DISSIPATIVE QUANTUM DYNAMICS 279
A. MODEL SYSTEMS 279
B. WIGNER-JVEISSKOPF THEORY AND QUANTUM
MEASUREMENTS 281
C. QUANTUM LANGEVIN EQUATION 284
D. MASTER EQUATION 286
E. INFLUENCE FUNCTIONAL METHOD 288
3. DYNAMICAL LOCALIZATION IN THE DISSIPATIVE KICK*ROTOR
MODEL 295
A. QUANTUM MAP 295
B. SEMI-CLASSICAL LIMIT, QUANTUM NOISE 295
C. DYNAMICAL LOCALIZATION AND WEAK DISSIPATION 299
XIV
4. DYNAMICALLY LOCALIZED ELECTROMAGNETIC FIELD IN A HIGH-Q
CAVITY 305
5. RYDBERG ATOMS IN A NOISY WAVE-GUIDE 308
A. BASIC EFFECTS AND IDEAS FOR AN EXPERIMENT 308
B. THEORY 309
C. EXPERIMENT 314
6. DYNAMICAL LOCALIZATION IN THE PERIODICALLY DRIVEN
PENDULUM 314
A. CLASSICAL PENDULUM 315
B. QUANTIZED SYSTEM 318
C. COUPLING TO THE ENVIRONMENT 322
D. EXPERIMENTAL REALIZATION BY THE DEFLECTION OF
AN ATOMIC BEAM IN A MODULATED STANDING LIGHT
WAVE 323
E. DYNAMICAL LOCALIZATION IN JOSEPHSON
JUNCTIONS 325 |
| any_adam_object | 1 |
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| discipline | Physik |
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| spelling | Chaos and quantum chaos proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 W. Dieter Heiss (ed.) Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo ; Hong Kong ; Barcelona ; Budapest Springer 1992 XIV, 330 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in physics 411 Literaturangaben Chaostheorie (DE-588)4009754-7 gnd rswk-swf Chaos (DE-588)4191419-3 gnd rswk-swf Quantenchaos (DE-588)4130849-9 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1992 Blydepoort gnd-content Quantenchaos (DE-588)4130849-9 s DE-604 Chaostheorie (DE-588)4009754-7 s Chaos (DE-588)4191419-3 s Heiss, Walter D. edt Chris Engelbrecht Summer School on Theoretical Physics 8 1992 Blydepoort Sonstige (DE-588)2126322-X oth Lecture notes in physics 411 (DE-604)BV000003166 411 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019108538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chaos and quantum chaos proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 Lecture notes in physics Chaostheorie (DE-588)4009754-7 gnd Chaos (DE-588)4191419-3 gnd Quantenchaos (DE-588)4130849-9 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4191419-3 (DE-588)4130849-9 (DE-588)1071861417 |
| title | Chaos and quantum chaos proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 |
| title_auth | Chaos and quantum chaos proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 |
| title_exact_search | Chaos and quantum chaos proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 |
| title_full | Chaos and quantum chaos proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 W. Dieter Heiss (ed.) |
| title_fullStr | Chaos and quantum chaos proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 W. Dieter Heiss (ed.) |
| title_full_unstemmed | Chaos and quantum chaos proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 W. Dieter Heiss (ed.) |
| title_short | Chaos and quantum chaos |
| title_sort | chaos and quantum chaos proceedings of the eighth chris engelbrecht summer school on theoretical physics held at blydepoort eastern transvaal south africa 13 24 january 1992 |
| title_sub | proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics, held at Blydepoort, Eastern Transvaal, South Africa, 13 - 24 January 1992 |
| topic | Chaostheorie (DE-588)4009754-7 gnd Chaos (DE-588)4191419-3 gnd Quantenchaos (DE-588)4130849-9 gnd |
| topic_facet | Chaostheorie Chaos Quantenchaos Konferenzschrift 1992 Blydepoort |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019108538&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
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