Verfügbarkeit: Geometric phases in classical and quantum mechanics

Geometric phases in classical and quantum mechanics:

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Bibliographische Detailangaben
Beteiligte Personen:	Chruściński, Dariusz (VerfasserIn), Jamiołkowski, Andrzej 1946- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Boston [u.a.] Birkhäuser 2004
Schriftenreihe:	Progress in mathematical physics 36
Schlagwörter:	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
Links:	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
Umfang:	XII, 333 S. graph. Darst.
ISBN:	081764282X 9780817642822

Internformat

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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
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author	Chruściński, Dariusz Jamiołkowski, Andrzej 1946-
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series2	Progress in mathematical physics
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
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work_keys_str_mv	AT chruscinskidariusz geometricphasesinclassicalandquantummechanics AT jamiołkowskiandrzej geometricphasesinclassicalandquantummechanics

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