Nonlinear dynamics and quantum chaos: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer
2014
|
| Schriftenreihe: | Graduate texts in physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 206 S. Ill., graph. Darst. |
| ISBN: | 9783319063423 |
Internformat
MARC
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| 008 | 140611s2014 ad|| |||| 00||| eng d | ||
| 020 | |a 9783319063423 |c print |9 978-3-319-06342-3 | ||
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| 245 | 1 | 0 | |a Nonlinear dynamics and quantum chaos |b an introduction |c Sandro Wimberger |
| 264 | 1 | |a Cham [u.a.] |b Springer |c 2014 | |
| 300 | |a XIII, 206 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Graduate texts in physics | |
| 650 | 0 | 7 | |a Nichtlineare Dynamik |0 (DE-588)4126141-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenchaos |0 (DE-588)4130849-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nichtlineare Dynamik |0 (DE-588)4126141-0 |D s |
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-319-06343-0 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027347232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027347232 | ||
Datensatz im Suchindex
| _version_ | 1804152260494622720 |
|---|---|
| adam_text | Contents
1
Introduction
........................................ 1
1.1 Fundamental
Terminology
........................... 1
1.2
Complexity
......................................
З
1.3
Classical Versus Quantum Dynamics
.................... 5
Problems
........................................... 6
References
.......................................... 7
2
Dynamical Systems
................................... 9
2.1
Evolution Law
................................... 9
2.2
One-Dimensional Maps
............................. 11
2.2.1
The Logistic Map
............................ 11
2.2.2
The Dyadic Map
............................. 15
2.2.3
Deterministic Random Number Generators
........... 17
Problems
........................................... 18
References
.......................................... 18
3
Nonlinear Hamiltonian Systems
.......................... 21
3.1
integrable
Examples
................................ 21
3.2
Hamiltonian Formalism
............................. 25
3.3
Important Techniques in the Hamiltonian Formalism
......... 27
3-3.1
Conserved Quantity
H
......................... 27
3.3.2
Canonical Transformations
...................... 28
3.3.3
Liouville s Theorem
.......................... 31
3.3.4
Hamilton—Jacobi Theory and Action-Angle Variables
... 33
3.4
Integrable
Systems
................................. 36
3.4.1
Examples
.................................. 38
3.4.2
Poisson
Brackets and Constants of Motion
........... 39
3.5
Non-integrable
Systems
............................. 40
3.6
Perturbation of Low-Dimensional Systems
................ 40
3.6-1
Adiabatic Invariants
.......................... 40
3.6.2
Principle of Averaging
......................... 43
3.7
Canonical Perturbation Theory
........................ 47
3.7.1
Statement of the Problem
....................... 47
3.7.2
One-Dimensional Case
........................ 48
Xi
xii
Contents
3.7.3
Problem of Small Divisors
...................... 51
3.7.4 KAM
Theorem
.............................. 52
3.7.5
Example: Two Degrees of Freedom
............... 55
3.7.6
Secular Perturbation Theory
..................... 56
3.8
Transition to Chaos in Hamiltoman Systems
............... 60
3.8.1
Surface of Sections
........................... 60
3.8.2
Pome
aré—
C artan
Theorem
...................... 62
3.8.3
Area Preserving Maps
......................... 65
3.8.4
Fixed Points
................................ 67
3.8.5
Poincaré—
Birkhoff Theorem
..................... 71
3.8.6
Dynamics Near Unstable Fixed Points
.............. 73
3.8.7
Mixed Regular-Chaotic Phase Space
............... 78
3.9
Criteria for Local and Global Chaos
.................... 81
3.9.1
Ergodocity and Mixing
........................ 84
3.9.2
The Maximal Lyapunov Exponent
................ 87
3.9.3
Numerical Computation of the Maximal
Lyapunov Exponent
.......................... 90
3.9.4
The Lyapunov Spectrum
....................... 92
3.9.5
Kolmogorov-Sinai Entropy
..................... 94
3.9.6
Resonance Overlap Criterion
.................... 95
Appendix
........................................... 98
Problems
........................................... 98
References
.......................................... 100
4
Aspects of Quantum Chaos
............................. 103
4.1
Introductory Remarks on Quantum Mechanics
............. 103
4.2
Semiclassical
Quantization of
Integrable
Systems
........... 105
4.2.1
Bohr-Sommerfeld Quantization
.................. 105
4.2.2
Wentzel—Kramer—Briilouin—Jeffreys Approximation
.... 106
4.2.3
Einstein— Keller—
Brillouin
Quantization
............. 119
4.2.4
Semiclassical Wave Function for Higher Dimensional
Integrable
Systems
............................ 122
4.3
Semiclassical Description of
Non-inte
grabie
Systems
......... 126
4.3.1
Green s Functions
............................ 126
4.3.2
Feynman Path Integral
......................... 128
4.3.3
Method of Stationary Phase
..................... 130
4.3.4
Van Vleck Propagator
......................... 132
4.3.5
Semiclassical Green s Function
................... 134
4.3.6
Gutzwiller s Trace Formula
..................... 136
4.3.7
Applications of Semiclassical Theory
.............. 141
4.4
Wave Functions in Phase Space
....................... 149
4.4.1
Phase Space Densities
......................... 149
4.4.2
Weyl Transform and Wigner Function
.............. 150
4.4.3
Localization Around Classical Phase Space Structures.
. . 155
Contents
хні
4.5 Anderson
and Dynamical Localization
................... 159
4.5.1
Anderson Localization
......................... 160
4.5.2
Dynamical Localization in Periodically Dnven
Quantum Systems
............................ 163
4.5.3
Experiments
................................ 167
4.6
Universal Level Statistics
............................ 168
4.6.1
Level Repulsion: Avoided Crossings
............... 169
4.6.2
Level Statistics
.............................. 170
4.6.3
Symmetries and Constants of Motion
.............. 171
4.6.4
Density of States and Unfolding of Spectra
.......... 173
4.6.5
Nearest Neighbor Statistics for
Integrable
Systems
..... 174
4.6.6
Nearest Neighbor Statistics for Chaotic Systems
....... 176
4.6.7
Gaussian Ensembles of Random Matrices
........... 179
4.6.8
More Sophisticated Methods
.................... 184
4.7
Concluding Remarks
............................... 188
Appendix
........................................... 1 89
Problems
........................................... 190
References
.......................................... 199
Index
................................................ 203
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T01:07:53Z |
| institution | BVB |
| isbn | 9783319063423 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027347232 |
| oclc_num | 883967311 |
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| physical | XIII, 206 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
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| series2 | Graduate texts in physics |
| spelling | Wimberger, Sandro 1974- Verfasser (DE-588)128781262 aut Nonlinear dynamics and quantum chaos an introduction Sandro Wimberger Cham [u.a.] Springer 2014 XIII, 206 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in physics Nichtlineare Dynamik (DE-588)4126141-0 gnd rswk-swf Quantenchaos (DE-588)4130849-9 gnd rswk-swf Nichtlineare Dynamik (DE-588)4126141-0 s DE-604 Quantenchaos (DE-588)4130849-9 s Erscheint auch als Online-Ausgabe 10.1007/978-3-319-06343-0 Erscheint auch als Online-Ausgabe 978-3-319-06343-0 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027347232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wimberger, Sandro 1974- Nonlinear dynamics and quantum chaos an introduction Nichtlineare Dynamik (DE-588)4126141-0 gnd Quantenchaos (DE-588)4130849-9 gnd |
| subject_GND | (DE-588)4126141-0 (DE-588)4130849-9 |
| title | Nonlinear dynamics and quantum chaos an introduction |
| title_auth | Nonlinear dynamics and quantum chaos an introduction |
| title_exact_search | Nonlinear dynamics and quantum chaos an introduction |
| title_full | Nonlinear dynamics and quantum chaos an introduction Sandro Wimberger |
| title_fullStr | Nonlinear dynamics and quantum chaos an introduction Sandro Wimberger |
| title_full_unstemmed | Nonlinear dynamics and quantum chaos an introduction Sandro Wimberger |
| title_short | Nonlinear dynamics and quantum chaos |
| title_sort | nonlinear dynamics and quantum chaos an introduction |
| title_sub | an introduction |
| topic | Nichtlineare Dynamik (DE-588)4126141-0 gnd Quantenchaos (DE-588)4130849-9 gnd |
| topic_facet | Nichtlineare Dynamik Quantenchaos |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027347232&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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