Classical Nonintegrability, Quantum Chaos: With a contribution by Viviane Baladi
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1997
|
| Schriftenreihe: | DMV Seminar
27 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonintegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schrödinger equation. Scattering by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close |
| Beschreibung: | 1 Online-Ressource (VI, 102 p.) 7 illus |
| ISBN: | 9783034889322 9783764357085 |
| DOI: | 10.1007/978-3-0348-8932-2 |
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| 490 | 1 | |a DMV Seminar |v 27 | |
| 500 | |a Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonintegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schrödinger equation. Scattering by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close | ||
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Datensatz im Suchindex
| _version_ | 1804153096451915776 |
|---|---|
| any_adam_object | |
| author | Knauf, Andreas |
| author_GND | (DE-588)1017305048 (DE-588)124663079 (DE-588)1089188501 |
| author_facet | Knauf, Andreas |
| author_role | aut |
| author_sort | Knauf, Andreas |
| author_variant | a k ak |
| building | Verbundindex |
| bvnumber | BV042422261 |
| classification_tum | MAT 000 |
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| dewey-ones | 510 - Mathematics |
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| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8932-2 |
| format | Electronic eBook |
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| id | DE-604.BV042422261 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034889322 9783764357085 |
| language | English |
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| spelling | Knauf, Andreas Verfasser (DE-588)1017305048 aut Classical Nonintegrability, Quantum Chaos With a contribution by Viviane Baladi by Andreas Knauf, Yakov G. Sinai, Viviane Baladi Basel Birkhäuser Basel 1997 1 Online-Ressource (VI, 102 p.) 7 illus txt rdacontent c rdamedia cr rdacarrier DMV Seminar 27 Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonintegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schrödinger equation. Scattering by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close Mathematics Mathematics, general Mathematik Quantenchaos (DE-588)4130849-9 gnd rswk-swf Zetafunktion (DE-588)4190764-4 gnd rswk-swf Streutheorie (DE-588)4183697-2 gnd rswk-swf Zetafunktion (DE-588)4190764-4 s 1\p DE-604 Quantenchaos (DE-588)4130849-9 s 2\p DE-604 Streutheorie (DE-588)4183697-2 s 3\p DE-604 Sinaj, Jakov G. 1935- Sonstige (DE-588)124663079 oth Baladi, Viviane 1963- Sonstige (DE-588)1089188501 oth DMV Seminar 27 (DE-604)BV000020322 27 https://doi.org/10.1007/978-3-0348-8932-2 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Knauf, Andreas Classical Nonintegrability, Quantum Chaos With a contribution by Viviane Baladi DMV Seminar Mathematics Mathematics, general Mathematik Quantenchaos (DE-588)4130849-9 gnd Zetafunktion (DE-588)4190764-4 gnd Streutheorie (DE-588)4183697-2 gnd |
| subject_GND | (DE-588)4130849-9 (DE-588)4190764-4 (DE-588)4183697-2 |
| title | Classical Nonintegrability, Quantum Chaos With a contribution by Viviane Baladi |
| title_auth | Classical Nonintegrability, Quantum Chaos With a contribution by Viviane Baladi |
| title_exact_search | Classical Nonintegrability, Quantum Chaos With a contribution by Viviane Baladi |
| title_full | Classical Nonintegrability, Quantum Chaos With a contribution by Viviane Baladi by Andreas Knauf, Yakov G. Sinai, Viviane Baladi |
| title_fullStr | Classical Nonintegrability, Quantum Chaos With a contribution by Viviane Baladi by Andreas Knauf, Yakov G. Sinai, Viviane Baladi |
| title_full_unstemmed | Classical Nonintegrability, Quantum Chaos With a contribution by Viviane Baladi by Andreas Knauf, Yakov G. Sinai, Viviane Baladi |
| title_short | Classical Nonintegrability, Quantum Chaos |
| title_sort | classical nonintegrability quantum chaos with a contribution by viviane baladi |
| title_sub | With a contribution by Viviane Baladi |
| topic | Mathematics Mathematics, general Mathematik Quantenchaos (DE-588)4130849-9 gnd Zetafunktion (DE-588)4190764-4 gnd Streutheorie (DE-588)4183697-2 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Quantenchaos Zetafunktion Streutheorie |
| url | https://doi.org/10.1007/978-3-0348-8932-2 |
| volume_link | (DE-604)BV000020322 |
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