Geometric phases in classical and quantum mechanics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
2004
|
| Schriftenreihe: | Progress in mathematical physics
36 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 333 S. graph. Darst. |
| ISBN: | 081764282X 9780817642822 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | DARIUSZ CHRUSCINSKI ANDRZEJ JAMIOLKOWSKI GEOMETRIC PHASES IN CLASSICAL
AND QUANTUM MECHANICS BIRKHAUSER BOSTON * BASEL * BERLIN CONTENTS
PREFACE IX 1 MATHEMATICAL BACKGROUND 1 1.1 MANIFOLDS, FORMS AND ALL THAT
1 1.1.1 BASIC NOTIONS 1 1.1.2 DIFFERENTIAL FORMS 6 1.1.3 INTEGRATION OF
FORMS 9 1.1.4 DE RHAM COHOMOLOGY 12 1.1.5 LIE DERIVATIVE 15 1.2 GROUPS,
LIE ALGEBRAS AND ACTIONS 17 1.2.1 BASIC DEFINITIONS 17 1.2.2 ACTIONS OF
LIE GROUPS 19 1.2.3 HOMOGENEOUS SPACES 23 1.2.4 LIE ALGEBRAS AND
DIFFERENTIAL FORMS 25 1.3 BUNDLES AND CONNECTIONS 29 1.3.1 FIBRE BUNDLE
29 1.3.2 EXAMPLES OF FIBRE BUNDLES 34 1.3.3 CONNECTIONS * GENERAL THEORY
37 1.3.4 CONNECTION IN A-PRINCIPAL BUNDLE 41 1.3.5 GAUGE TRANSFORMATIONS
* PAVING THE WAY TO PHYSICS 45 1.3.6 CHARACTERISTIC CLASSES 50 1.4
TOPOLOGY, BUNDLES AND PHYSICS 53 1.4.1 ELEMENTS FROM HOMOTOPY THEORY 53
VI CONTENTS 1.4.2 MONOPOLE BUNDLE 57 1.4.3 INSTANTON BUNDLE 61 1.4.4
HOPF FIBRATION S 3 ** S 2 63 1.4.5 HOPF FIBRATION S 1 -^- S 4 67
PROBLEMS 69 2 ADIABATIC PHASES IN QUANTUM MECHANICS 73 2.1 ADIABATIC
EVOLUTION IN QUANTUM MECHANICS 73 2.1.1 ADIABATIC APPROACH OF BORN AND
FOCK 73 2.1.2 ADIABATIC THEOREM 76 2.1.3 ADIABATICITY AND GEOMETRY 78
2.2 BERRY S PHASE 79 2.2.1 PHASE IN QUANTUM MECHANICS 79 2.2.2 STANDARD
DERIVATION 80 2.2.3 HOW TO MEASURE THE BERRY PHASE 84 2.2.4 BERRY-SIMON
CONNECTION 85 2.2.5 EXAMPLES 86 2.2.6 QUANTUM GEOMETRIC TENSOR 94 2.2.7
QUANTAL PHASE AND GEOMETRY * A SIMPLE ILLUSTRATION 96 2.3 NON-ABELIAN
WILCZEK-ZEE PHASE 100 2.3.1 STANDARD DERIVATION 100 2.3.2 FIBRE BUNDLE
APPROACH 101 2.3.3 NON-ABELIAN PHASE IN QUADRUPOLE RESONANCE 105
PROBLEMS 108 3 ADIABATIC PHASES IN CLASSICAL MECHANICS 111 3.1
HAMILTONIAN SYSTEMS ILL 3.1.1 WHAT WE MEAN BY A PHASE IN CLASSICAL
MECHANICS ILL 3.1.2 SYMPLECTIC GEOMETRY AND HAMILTONIAN DYNAMICS 113
3.1.3 INTEGRABLE SYSTEMS 117 3.2 ADIABATIC PHASE OF HANNAY 121 3.2.1
AVERAGING PRINCIPLE 121 3.2.2 ADIABATIC INVARIANTS 123 3.2.3 HANNAY S
ANGLES 128 3.2.4 BERRY S PHASE VERSUS HANNAY S ANGLE 130 3.3 CLASSICAL
GEOMETRIC PHASES - EXAMPLES 132 3.3.1 CLASSICAL SPIN 132 3.3.2
CLASSICAL OSCILLATOR 136 3.3.3 ROTATED ROTATOR (HANNAY S HOOP) 138 3.3.4
MOTION IN NON-INERTIAL FRAMES 142 3.3.5 GUIDING CENTER MOTION 146 3.3.6
RIGID BODIES AND THE GEOMETRIC PHASE 149 PROBLEMS 154 CONTENTS VII 4
GEOMETRIC APPROACH TO CLASSICAL PHASES 157 4.1 HAMILTONIAN SYSTEMS WITH
SYMMETRIES 157 4.1.1 HAMILTONIAN ACTIONS AND MOMENTUM MAPS . 157 4.1.2
REDUCED PHASE SPACE 160 4.2 GEOMETRIC APPROACH TO ADIABATIC PHASES 163
4.2.1 FAMILIES OF HAMILTONIAN ACTIONS 163 4.2.2 HANNAY S ANGLES AND THE
HANNAY-BERRY CONNECTION 165 4.3 REDUCTION, RECONSTRUCTION AND PHASES 168
4.3.1 RECONSTRUCTION OF DYNAMICS 168 4.3.2 RIGID BODIES . 173 PROBLEMS
178 5 GEOMETRY OF QUANTUM EVOLUTION 179 5.1 GEOMETRICAL FORMULATION OF
QUANTUM MECHANICS 179 5.1.1 HILBERT SPACE AS A KAHLER MANIFOLD 179 5.1.2
THE QUANTUM PHASE SPACE 184 5.1.3 EXAMPLE: GEOMETRY OF CP 187 5.1.4
SYMPLECTIC STRUCTURE AND QUANTUM DYNAMICS 190 5.1.5 METRIC STRUCTURE AND
UNCERTAINTY RELATION 193 5.2 AHARONOV-ANANDAN PHASE 196 5.2.1 STANDARD
DERIVATION 196 5.2.2 EXAMPLE: SPIN-HALF IN A MAGNETIC FIELD 200 5.2.3
FIBRE BUNDLE APPROACH 202 5.2.4 GEOMETRY OF CP AND AHARONOV-ANANDAN
PHASE 204 5.3 QUANTUM MEASUREMENT AND PANCHARATNAM PHASE 205 5.3.1
GEODESIES IN QUANTUM PHASE SPACE 205 5.3.2 DISTANCE BETWEEN PURE QUANTUM
STATES 208 5.3.3 MEASUREMENT PROCESS 211 5.3.4 PANCHARATNAM PHASE 213
5.4 -GEOMETRIC PHASE FOR MIXED STATES 218 5.4.1 MIXED STATES IN QUANTUM
MECHANICS 218 5.4.2 UHLMANN S NON-ABELIAN GEOMETRIC FACTOR 221 5.4.3
DISTANCE BETWEEN MIXED STATES 227 5.4.4 HOW TO MEASURE GEOMETRIC PHASE
232 PROBLEMS 236 6 GEOMETRIC PHASES IN ACTION 239 6.1 OPTICAL
MANIFESTATION OF GEOMETRIC PHASES 239 6.1.1 SPINS AND HELICITIES 239
6.1.2 CHIAO-TOMITA-^WU PHASE 242 6.1.3 RYTOV S LAW AND FERMI-WALKER
TRANSPORT 243 6.1.4 PANCHARATNAM PHASE 247 6.2 QUANTUM MECHANICS AS A
GAUGE THEORY 249 6.2.1 CLASSICAL PARTICLES IN GAUGE THEORY 250 VIII
CONTENTS 6.2.2 [/(L)-INVARIANCE AND THE AHARONOV-BOHM EFFECT 251 6.2.3
SF/(2)-INVARIANCE AND THE AHARONOV-CASHER EFFECT 254 6.3 PHASES IN
MOLECULAR PHYSICS 258 6.3.1 DEGENERACIES 258 6.3.2 TIME-REVERSAL
INVARIANT FERMIONIC SYSTEM 261 6.3.3 BORN-OPPENHEIMER APPROXIMATION 266
6.3.4 DIATOMIC MOLECULE 269 6.3.5 QUANTUM GEOMETRIC FORCES 271 6.4 THE
QUANTUM HALL EFFECT 274 6.4.1 PRELIMINARIES 274 6.4.2 QUANTUM DYNAMICS
IN A MAGNETIC FIELD 277 6.4.3 FIBRE BUNDLE APPROACH TO THE QHE 279 6.5
SPIN, STATISTICS AND THE GEOMETRIC PHASE 281 6.5.1 THE TRANSPORTED SPIN
BASIS 282 6.5.2 SCHWINGER REPRESENTATION 285 6.5.3 EXCHANGE ROTATION 288
6.5.4 PAULI SIGN AS A TOPOLOGICAL PHASE 292 6:6 ENTANGLEMENT AND
HOLONOMIC QUANTUM COMPUTATION 293 6.6.1 COMPOSITE SYSTEMS AND ENTANGLED
STATES 293 6:6.2 QUBITS AND BUNDLES 295 6.6.3 QUANTUM COMPUTER * AN
OVERVIEW 297 6.6.4 HOLONOMIC QUANTUM COMPUTATION 300 PROBLEMS 303 A
CLASSICAL MATRIX LIE GROUPS AND ALGEBRAS 305 B QUATERNIONS 307
BIBLIOGRAPHY 311 INDEX 329
|
| any_adam_object | 1 |
| author | Chruściński, Dariusz Jamiołkowski, Andrzej 1946- |
| author_GND | (DE-588)124199771 (DE-588)140988661 |
| author_facet | Chruściński, Dariusz Jamiołkowski, Andrzej 1946- |
| author_role | aut aut |
| author_sort | Chruściński, Dariusz |
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| callnumber-subject | QC - Physics |
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| dewey-ones | 530 - Physics |
| dewey-raw | 530.12 |
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| id | DE-604.BV014894550 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:08:31Z |
| institution | BVB |
| isbn | 081764282X 9780817642822 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010070298 |
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| physical | XII, 333 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematical physics |
| series2 | Progress in mathematical physics |
| spelling | Chruściński, Dariusz Verfasser (DE-588)124199771 aut Geometric phases in classical and quantum mechanics Dariusz Chruściński ; Andrzej Jamiołkowski Boston [u.a.] Birkhäuser 2004 XII, 333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematical physics 36 Física matemática larpcal Holonomie gtt Kwantummechanica gtt Mathematische fysica gtt Mecânica quântica larpcal Natuurkunde gtt Phases quantiques géométriques Physique mathématique Théorie quantique Mathematische Physik Physik Quantentheorie Geometric quantum phases Mathematical physics Quantum theory Berry-Phase (DE-588)4296737-5 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Berry-Phase (DE-588)4296737-5 s Mathematische Physik (DE-588)4037952-8 s b DE-604 Jamiołkowski, Andrzej 1946- Verfasser (DE-588)140988661 aut Progress in mathematical physics 36 (DE-604)BV013823265 36 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010070298&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chruściński, Dariusz Jamiołkowski, Andrzej 1946- Geometric phases in classical and quantum mechanics Progress in mathematical physics Física matemática larpcal Holonomie gtt Kwantummechanica gtt Mathematische fysica gtt Mecânica quântica larpcal Natuurkunde gtt Phases quantiques géométriques Physique mathématique Théorie quantique Mathematische Physik Physik Quantentheorie Geometric quantum phases Mathematical physics Quantum theory Berry-Phase (DE-588)4296737-5 gnd Quantentheorie (DE-588)4047992-4 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4296737-5 (DE-588)4047992-4 (DE-588)4037952-8 |
| title | Geometric phases in classical and quantum mechanics |
| title_auth | Geometric phases in classical and quantum mechanics |
| title_exact_search | Geometric phases in classical and quantum mechanics |
| title_full | Geometric phases in classical and quantum mechanics Dariusz Chruściński ; Andrzej Jamiołkowski |
| title_fullStr | Geometric phases in classical and quantum mechanics Dariusz Chruściński ; Andrzej Jamiołkowski |
| title_full_unstemmed | Geometric phases in classical and quantum mechanics Dariusz Chruściński ; Andrzej Jamiołkowski |
| title_short | Geometric phases in classical and quantum mechanics |
| title_sort | geometric phases in classical and quantum mechanics |
| topic | Física matemática larpcal Holonomie gtt Kwantummechanica gtt Mathematische fysica gtt Mecânica quântica larpcal Natuurkunde gtt Phases quantiques géométriques Physique mathématique Théorie quantique Mathematische Physik Physik Quantentheorie Geometric quantum phases Mathematical physics Quantum theory Berry-Phase (DE-588)4296737-5 gnd Quantentheorie (DE-588)4047992-4 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Física matemática Holonomie Kwantummechanica Mathematische fysica Mecânica quântica Natuurkunde Phases quantiques géométriques Physique mathématique Théorie quantique Mathematische Physik Physik Quantentheorie Geometric quantum phases Mathematical physics Quantum theory Berry-Phase |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010070298&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013823265 |
| work_keys_str_mv | AT chruscinskidariusz geometricphasesinclassicalandquantummechanics AT jamiołkowskiandrzej geometricphasesinclassicalandquantummechanics |