Many-body Schrödinger Dynamics of Bose-Einstein Condensates:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2011
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| Series: | Springer Theses
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XII, 130 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642228650 3642228658 |
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IMAGE 1
CONTENTS
1 INTRODUCTION 1
1.1 THE PATH TO BOSE-EINSTEIN CONDENSATION 1
1.2 THEORIES FOR BOSE-EINSTEIN CONDENSATES 2
1.3 OVERVIEW OF THIS THESIS 4
REFERENCES 6
2 GENERAL THEORY 9
2.1 THE FIELD OPERATOR 9
2.2 THE MANY-BODY HAMILTONIAN 10
2.3 THE TIME-DEPENDENT VARIATIONAL PRINCIPLE 11
2.4 THE MANY-BOSON WAVE FUNCTION 12
2.5 REDUCED DENSITY MATRICES AND THEIR EIGENFUNCTIONS 14 2.6 TWO-BODY
EXPECTATION VALUES AND GEMINAIS 15
2.7 CORRELATION FUNCTIONS AND RDMS 16
2.8 DEFINITION AND SIGNATURES OF NTH ORDER COHERENCE 16
2.9 FIRST AND SECOND ORDER RDMS, CORRELATIONS AND COHERENCE . . 17 2.10
DEFINITION OF BOSE-EINSTEIN CONDENSATION AND FRAGMENTATION 20
2.11 CLASSIFICATION OF INTERACTING REGIMES OF TRAPPED BOSE-GASES 20
REFERENCES 22
3 GENERAL METHODS FOR THE QUANTUM DYNAMICS OF IDENTICAL BOSONS 23
3.1 MULTICONFIGURATIONAL TIME-DEPENDENT HARTREE FOR BOSONS 23 3.1.1
INTRODUCTION 23
3.1.2 THE MCTDHB WAVE FUNCTION 24
3.1.3 DERIVATION OF THE MCTDHB EQUATIONS 25
3.2 GROSS-PITAEVSKII THEORY 28
REFERENCES 30
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1013327322
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
4 LATTICE MODELS FOR THE QUANTUM DYNAMICS OF IDENTICAL BOSONS . 33 4.1
WANNIER FUNCTIONS OF A DOUBLE-WELL POTENTIAL 33
4.2 THE TWO-MODE GROSS-PITAEVSKII MODEL 34
4.3 THE BOSE-HUBBARD MODEL 35
REFERENCES 37
5 REDUCED DENSITY MATRICES AND COHERENCE OF TRAPPED INTERACTING BOSONS
39
5.1 INTRODUCTION 39
5.2 NUMERICAL METHODS 40
5.3 A GENERIC EXAMPLE OF A TRAPPED CONDENSATE 41
5.3.1 GENERAL REMARKS 41
5.3.2 TRAP PARAMETERS AND INTERACTION STRENGTH 41
5.3.3 CONDENSED STATE 42
5.3.4 FROM CONDENSATION TO FRAGMENTATION 46
5.3.5 FULLY FRAGMENTED STATE 47
5.4 FIRST-ORDER CORRELATIONS 48
5.4.1 GENERAL ANALYTICAL CONSIDERATIONS 48
5.4.2 NUMERICAL RESULTS 50
5.5 SECOND-ORDER CORRELATIONS 53
5.5.1 GENERAL ANALYTICAL CONSIDERATIONS 53
5.5.2 NUMERICAL RESULTS 56
5.6 CONCLUSIONS 61
REFERENCES 63
6 EXACT QUANTUM DYNAMICS OF A BOSONIC JOSEPHSON JUNCTION 65 6.1
INTRODUCTION 65
6.2 THEORIES FOR BOSONIC JOSEPHSON JUNCTIONS 66
6.2.1 EXACT MANY-BODY SCHROEDINGER DYNAMICS 66
6.2.2 BOSE-HUBBARD MANY-BODY DYNAMICS 66
6.2.3 GROSS-PITAEVSKII AND TWO-MODE GROSS-PITAEVSKII MEAN-FIELD DYNAMICS
67
6.3 OBSERVABLES OF THE BOSONIC JOSEPHSON JUNCTION 67
6.4 DETAILS OF THE BOSONIC JOSEPHSON JUNCTION 68
6.5 PREPARATION AND PROPAGATION OF THE MANY-BOSON WAVE FUNCTION 69
6.6 RESULTS FOR WEAK INTERACTIONS 70
6.6.1 BELOW THE SELF-TRAPPING TRANSITION POINT A A C 70
6.6.2 AROUND THE SELF-TRAPPING TRANSITION POINT A A C . . . 73 6.7
RESULTS FOR STRONGER INTERACTIONS 74
6.7.1 SELF-TRAPPING AT A 10A C 74
6.7.2 EQUILIBRATION AT A 25A C 77
6.8 CONCLUSIONS 79
REFERENCES 79
IMAGE 3
CONTENTS XI
7 QUANTUM DYNAMICS OF ATTRACTIVE VERSUS REPULSIVE BOSONIC JOSEPHSON
JUNCTIONS: BOESE-HUBBARD AND FULL-HAMILTONIAN RESULTS 81
7.1 INTRODUCTION 81
7.2 THEORY 82
7.2.1 THE BOSE-HUBBARD HAMILTONIAN 82
7.2.2 ATTRACTIVE-REPULSIVE SYMMETRY OF THE BOSE-HUBBARD HAMILTONIAN 82
7.2.3 SYMMETRY OF OBSERVABLES 83
7.3 BOSE-HUBBARD VERSUS FULL HAMILTONIAN EXACT RESULTS 84 REFERENCES 87
8 OPTIMAL TIME-DEPENDENT LATTICE MODELS FOR NONEQUILIBRIUM DYNAMICS 89
8.1 INTRODUCTION 89
8.2 THEORY 90
8.2.1 VARIATION WITH RESPECT TO THE COEFFICIENTS C~(T) 92 8.2.2
VARIATION WITH RESPECT TO THE LOCAL ORBITAL COEFFICIENTS D* K (T) 94
8.2.3 REMARKS ON THE TIME-DEPENDENT BOSE-HUBBARD MODEL 96
8.2.4 IMPLEMENTATION OF THE TIME-DEPENDENT BOSE-HUBBARD MODEL 97
8.3 EXAMPLE OF DYNAMICS USING TIME-DEPENDENT WANNIER FUNCTIONS 97
8.3.1 A DOUBLE-WELL POTENTIAL AS A TEST SYSTEM 97
8.3.2 QUANTUM QUENCH DYNAMICS IN A DOUBLE-WELL POTENTIAL 98
8.4 CONCLUSIONS 101
REFERENCES 102
9 FINAL REMARKS AND OUTLOOK 105
APPENDIX A: IMEST-ALGORITHM FOR ID, 2D AND 3D SYSTEMS 107
APPENDIX B: P-PARTICLE MOMENTUM DISTRIBUTION 115
APPENDIX C: MATRIX ELEMENTS OF THE 1ST AND 2ND ORDER RDMS 117
APPENDIX D: MATRIX ELEMENTS OF THE OPERATORS H - IF T AND W 119
APPENDIX E: BEST MEAN-FIELD 121
APPENDIX F: ON THE IMPORTANCE OF TIME-DEPENDENT BASIS SETS 123
IMAGE 4
XII CONTENTS
BIBLIOGRAPHY 127
BIOGRAPHY 129 |
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| spelling | Sakmann, Kaspar Verfasser (DE-588)141984325 aut Many-body Schrödinger Dynamics of Bose-Einstein Condensates Kaspar Sakmann Berlin [u.a.] Springer 2011 XII, 130 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Springer Theses Zugl.: Heidelberg, Univ., Diss., 2011 Schrödinger-Gleichung (DE-588)4053332-3 gnd rswk-swf Vielteilchentheorie (DE-588)4331960-9 gnd rswk-swf Gittermodell (DE-588)4226961-1 gnd rswk-swf Bose-Einstein-Kondensation (DE-588)4402897-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Bose-Einstein-Kondensation (DE-588)4402897-0 s Vielteilchentheorie (DE-588)4331960-9 s Schrödinger-Gleichung (DE-588)4053332-3 s Gittermodell (DE-588)4226961-1 s DE-604 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3850562&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024484122&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sakmann, Kaspar Many-body Schrödinger Dynamics of Bose-Einstein Condensates Schrödinger-Gleichung (DE-588)4053332-3 gnd Vielteilchentheorie (DE-588)4331960-9 gnd Gittermodell (DE-588)4226961-1 gnd Bose-Einstein-Kondensation (DE-588)4402897-0 gnd |
| subject_GND | (DE-588)4053332-3 (DE-588)4331960-9 (DE-588)4226961-1 (DE-588)4402897-0 (DE-588)4113937-9 |
| title | Many-body Schrödinger Dynamics of Bose-Einstein Condensates |
| title_auth | Many-body Schrödinger Dynamics of Bose-Einstein Condensates |
| title_exact_search | Many-body Schrödinger Dynamics of Bose-Einstein Condensates |
| title_full | Many-body Schrödinger Dynamics of Bose-Einstein Condensates Kaspar Sakmann |
| title_fullStr | Many-body Schrödinger Dynamics of Bose-Einstein Condensates Kaspar Sakmann |
| title_full_unstemmed | Many-body Schrödinger Dynamics of Bose-Einstein Condensates Kaspar Sakmann |
| title_short | Many-body Schrödinger Dynamics of Bose-Einstein Condensates |
| title_sort | many body schrodinger dynamics of bose einstein condensates |
| topic | Schrödinger-Gleichung (DE-588)4053332-3 gnd Vielteilchentheorie (DE-588)4331960-9 gnd Gittermodell (DE-588)4226961-1 gnd Bose-Einstein-Kondensation (DE-588)4402897-0 gnd |
| topic_facet | Schrödinger-Gleichung Vielteilchentheorie Gittermodell Bose-Einstein-Kondensation Hochschulschrift |
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