Quantum dynamical systems:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2001
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 278 S. graph. Darst. |
| ISBN: | 0198504004 |
Internformat
MARC
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| 100 | 1 | |a Alicki, Robert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum dynamical systems |c Robert Alicki ; Mark Fannes |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2001 | |
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Datensatz im Suchindex
| _version_ | 1804128693593833472 |
|---|---|
| adam_text | QUANTUM DYNAMICAL SYSTEMS ROBERT ALICKI INSTITUTE OF THEORETICAL PHYSICS
AND ASTROPHYSICS, UNIVERSITY OF GDANSK, POLAND AND MARK FANNES INSTITUUT
VOOR THEORETISCHE FYSICA, K. U. LEUVEN, BELGIUM OXFORD UNIVERSITY PRESS
CONTENTS 1 INTRODUCTION 1 2 BASIC TOOLS FOR QUANTUM MECHANICS 4 2.1
HILBERT SPACES AND OPERATORS 5 2.1.1 VECTOR SPACES 5 2.1.2 BANACH AND
HILBERT SPACES 7 2.1.3 GEOMETRICAL PROPERTIES OF HILBERT SPACES 9 2.1.4
ORTHONORMAL BASES 10 2.1.5 SUBSPACES AND PROJECTORS - 11 2.1.6 LINEAR
MAPS BETWEEN BANACH SPACES 13 2.1.7 LINEAR FUNCTIONALS AND DIRAC
NOTATION 14 2.1.8 ADJOINTS OF BOUNDED OPERATORS 18 2.1.9 HERMITIAN,
UNITARY AND NORMAL OPERATORS 19 2.1.10 PARTIAL ISOMETRIES AND POLAR
DECOMPOSITION 21 2.1.11 SPECTRA OF OPERATORS 22 2.1.12 UNBOUNDED
OPERATORS 24 2.2 MEASURES 25 2.2.1 MEASURES AND INTEGRATION 25 2.2.2
DISTRIBUTIONS 29 2.2.3 HILBERT SPACES OF FUNCTIONS 30 2.2.4 SPECTRAL
MEASURES 31 2.3 PROBABILITY IN QUANTUM MECHANICS 34 2.3.1 PURE STATES .
.35 2.3.2 MIXED STATES, DENSITY MATRICES 37 2.4 OBSERVABLES IN QUANTUM
MECHANICS 38 2.4.1 COMPACT OPERATORS 38 2.4.2 WEYL QUANTIZATION 40 2.5
COMPOSED SYSTEMS 44 2.5.1 DIRECT SUMS 45 2.5.2 TENSOR PRODUCTS 46 2.5.3
OBSERVABLES AND STATES OF COMPOSITE SYSTEMS 48 2.6 NOTES 53 3
DETERMINISTIC DYNAMICS 54 3.1 DETERMINISTIC QUANTUM DYNAMICS 55 3.1.1
TIME-INDEPENDENT HAMILTONIANS 55 3.1.2 PERTURBATIONS OF HAMILTONIANS 57
3.1.3 TIME-DEPENDENT HAMILTONIANS 58 3.1.4 PERIODIC PERTURBATIONS AND
FLOQUET OPERATORS 59 XI CONTENTS 3.1.5 KICKED DYNAMICS 61 3.2 CLASSICAL
LIMITS 62 3.3 CLASSICAL DIFFERENTIABLE DYNAMICS . . 66 3.4 SELF-ADJOINT
LAPLACIANS ON COMPACT MANIFOLDS 70 3.5 NOTES 72 SPIN CHAINS 73 4.1 LOCAL
OBSERVABLES 73 4.2 STATES OF A SPIN SYSTEM 75 4.3 SYMMETRIES AND
DYNAMICS 77 ALGEBRAIC TOOLS 82 5.1 C*-ALGEBRAS 82 5.2 EXAMPLES 87 5.3
STATES AND REPRESENTATIONS 90 5.4 DYNAMICAL SYSTEMS AND VON NEUMANN
ALGEBRAS 96 5.5 NOTES 102 FERMIONIC DYNAMICAL SYSTEMS 103 6.1 FERMIONS
IN FOCK SPACE 103 6.1.1 FOCK SPACE 103 6.1.2 CREATION AND ANNIHILATION
105 6.1.3 SECOND QUANTIZATION 108 6.2 THE CAR-ALGEBRA 113 6.2.1
CANONICAL ANTICOMMUTATION RELATIONS 113 6.2.2 QUASI-FREE AUTOMORPHISMS
114 6.2.3 QUASI-FREE STATES 117 6.3 NOTES 121 ERGODIC THEORY 122 7.1
ERGODICITY IN CLASSICAL SYSTEMS ; . 122, 7.2 ERGODICITY IN QUANTUM
SYSTEMS 125 7.2.1 ASYMPTOTIC ABELIANNESS 125 7.2.2 MULTITIME
CORRELATIONS 132 7.2.3 FLUCTUATIONS AROUND ERGODIC MEANS 135 7.3
LYAPUNOV EXPONENTS 139 7.3.1 CLASSICAL DYNAMICS * 140 7.3.2 QUANTUM
DYNAMICS 143 7.4 NOTES 144 QUANTUM IRREVERSIBILITY 146 8.1 MEASUREMENT
THEORY 146 8.2 OPEN QUANTUM SYSTEMS 151 8.3 COMPLETE POSITIVITY 153 8.4
QUANTUM DYNAMICAL SEMIGROUPS 160 8.5 QUASI-FREE COMPLETELY POSITIVE MAPS
164 CONTENTS 8.6 NOTES , 167 9 ENTROPY 169 9.1 VON NEUMANN ENTROPY
171 9.1.1 TECHNICAL PRELIMINARIES 171 9.1.2 PROPERTIES OF VON NEUMANN S
ENTROPY 174 9.1.3 MEAN ENTROPY 176 9.1.4 ENTROPY OF QUASI-FREE STATES
178 9.2 RELATIVE ENTROPY 181 9.2.1 FINITE-DIMENSIONAL CASE 181 9.2.2
MAXIMUM ENTROPY PRINCIPLE 182 9.2.3 ALGEBRAIC SETTING 184 9.3 NOTES 185
10 DYNAMICAL ENTROPY 186 10.1 OPERATIONAL PARTITIONS 188 10.2 DYNAMICAL
ENTROPY 195 10.2.1 SYMBOLIC DYNAMICS 195 10.2.2 THE ENTROPY 197 10.3
SOME TECHNICAL RESULTS 200 10.4 EXAMPLES 205 10.4.1 THE QUANTUM SHIFT
205 10.4.2 THE FREE SHIFT 207 10.4.3 INFINITE ENTROPY , 208 10.4.4
POWERS-PRICE SHIFTS 209 10.5 NOTES 211 11 CLASSICAL DYNAMICAL ENTROPY
213 11.1 THE KOLMOGOROV-SINAI INVARIANT . 213 11.2 H-DENSITY 218 12
FINITE QUANTUM SYSTEMS 225 12.1 QUANTUM CHAOS 225 12.1.1 TIME SCALES 226
12.1.2 SPECTRAL STATISTICS 226 12.1.3 SEMI-CLASSICAL LIMITS 227 12.2 THE
KICKED TOP 227 12.2.1 THE MODEL 227 12.2.2 THE CLASSICAL LIMIT 228
12.2.3 KICKED MEAN-FIELD HEISENBERG MODEL 228 12.2.4 CHAOTIC PROPERTIES
229 12.3 GRAM MATRICES 230 12.4 ENTROPY PRODUCTION 235 12.5 NOTES 238 13
MODEL SYSTEMS 240 CONTENTS 13.1 ENTROPY OF THE QUANTUM CAT MAP 240 13.2
RUELLE S INEQUALITY 243 13.2.1 NON-COMMUTATIVE RIEMANNIAN STRUCTURES 244
13.2.2 NON-COMMUTATIVE LYAPUNOV EXPONENTS 246 13.2.3 RUELLE S INEQUALITY
247 13.2.4 EXAMPLES 248 13.3 QUASI-FREE FERMION DYNAMICS 249 13.3.1
DESCRIPTION OF THE MODEL 250 13.3.2 MAIN RESULT , 251 13.3.3 SKETCH OF
THE PROOF 251 13.4 NOTES 256 14 EPILOGUE 257 REFERENCES 259 INDEX 269
|
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| author | Alicki, Robert Fannes, Mark |
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| discipline | Physik Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:18Z |
| institution | BVB |
| isbn | 0198504004 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009479485 |
| oclc_num | 248041732 |
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| physical | XIV, 278 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Oxford Univ. Press |
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| spelling | Alicki, Robert Verfasser aut Quantum dynamical systems Robert Alicki ; Mark Fannes 1. publ. Oxford [u.a.] Oxford Univ. Press 2001 XIV, 278 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dynamisches System - Quantenmechanik - Ergodentheorie Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 s Dynamisches System (DE-588)4013396-5 s DE-604 Fannes, Mark Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009479485&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alicki, Robert Fannes, Mark Quantum dynamical systems Dynamisches System - Quantenmechanik - Ergodentheorie Quantenmechanik (DE-588)4047989-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4047989-4 (DE-588)4013396-5 |
| title | Quantum dynamical systems |
| title_auth | Quantum dynamical systems |
| title_exact_search | Quantum dynamical systems |
| title_full | Quantum dynamical systems Robert Alicki ; Mark Fannes |
| title_fullStr | Quantum dynamical systems Robert Alicki ; Mark Fannes |
| title_full_unstemmed | Quantum dynamical systems Robert Alicki ; Mark Fannes |
| title_short | Quantum dynamical systems |
| title_sort | quantum dynamical systems |
| topic | Dynamisches System - Quantenmechanik - Ergodentheorie Quantenmechanik (DE-588)4047989-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamisches System - Quantenmechanik - Ergodentheorie Quantenmechanik Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009479485&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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