Transport of Bose-Einstein condensates through two dimensional cavities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Regensburg
Univ.-Verl.
2015
|
| Edition: | 1. Aufl. |
| Series: | Dissertationsreihe Physik
44 |
| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-312262 Inhaltsverzeichnis |
| Physical Description: | VII, 217 S. graph. Darst. |
| ISBN: | 3868451196 9783868451191 |
Staff View
MARC
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| 100 | 1 | |a Hartmann, Timo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Transport of Bose-Einstein condensates through two dimensional cavities |c Timo Hartmann |
| 250 | |a 1. Aufl. | ||
| 264 | 1 | |a Regensburg |b Univ.-Verl. |c 2015 | |
| 300 | |a VII, 217 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Record in the Search Index
| _version_ | 1804153264311107584 |
|---|---|
| adam_text | CONTENTS
1 INTRODUCTION 1
2 THE BOSE-EINSTEIN CONDENSATE 7
2.1 THE MEAN-FIELD EQUATION FOR CONDENSATES 7
2.1.1 ENERGY MINIMIZATION USING CHE HARTREE ANSATZ 7
2.1.2 THE SECOND QUANTIZATION 9
2.1.3 PARTICLE-PARTICLE INTERACTION 11
2.2 EXTERNAL POTENTIALS FOR BOSE-EINSTEIN CONDENSATES 12
2.2.1 OPTICA! POTENTIALS 12
2.2.2 EXTERNAL POTENTIALS INDUCED BY MAGNETIC FIELDS 13
2.2.3 RESTRICTION TO TWO DIMENSIONS 14
2.3 GAUGE POTENTIALS FOR BOSE-EINSTEIN CONDENSATES 15
2.4 SUMMARY 17
3 STATIONARY SCATTERING STATES OF THE SCHROEDINGER EQUATION 19
3.1 INTRODUCTION 19
3.2 THE RETARDED GREEN FUNCTION 20
3.3 THE TIGHT BINDING MODEL 21
3.4 THE TIGHT BINDING MODEL FOR A CONSTANT POTENTIAL 22
3.4.1 EIGENFUNCTIONS FOR A CONSTANT POTENTIAL 22
3.4.2 A SOURCE ON AN INFINITE LATTICE 23
3.4.3 CALCULATION OF THE CURRENT 25
3.4.4 A SOURCE IN AN SEMI-INFINITE STRIP 26
3.5 THE GREEN FUNCTION IN THE TIGHT BINDING MODEL 28
3.5.1 HANDLING OF THE LEFT LEAD 29
3.5.2 CALCULATION OF THE SEIF ENERGY 30
3.5.3 HANDLING OF THE RIGHT LEAD 32
3.6 GENERALIZATION TO TWO DIMENSIONS 33
3.6.1 THE TWO DIMENSIONALLEADS 34
3.6.2 CURRENT MEASUREMENT IN TWO DIMENSIONS 36
3.6.3 MAGNETIC GAUGE FIELD 36
3.6.4 SELECTION OF THE GAUGE FIELD 37
3.7 EXTERIOR COMPLEX SCALING BOUNDARY CONDITIONS 38
3.7.1 ACCURACY OF THE EXTERIOR COMPLEX SCALING BOUNDARY CONDITIONS 42
3.7.2 RESONANCES 43
3.8 SCATTERING
SYSTEMS
OF BILLIARD
TYPE
47
HTTP://D-NB.INFO/1063374480
VI
CONTENTS
3.8.1 B . AN ALMOST-CLOSED EXAMPLE SYSTEM 48
3.9 COMPUTATIONAL COMPLEXITY 50
3.10 SUMMARY, OUTLOOK AND OPEN ENDS 52
4 SIMULATION OF THE TIME DEPENDENT GROSS-PITAEVSKII EQUATION 53
4.1 INTRODUCTION 53
4.2 CRANK-NICHOLSON 54
4.3 INCORPORATING THE INTERACTION TERM 56
4.4 THE TAYLOR SERIES METHOD 57
4.5 THE SPLIT
OPERATOR
METHOD 59
4.6 ACCURACY OF THE EXTERIOR COMPLEX SCALING BOUNDARY CONDITIONS 61
4.7 NON-ADIABATIC SWITCHING OF THE SOURCE 62
5 STATIONARY SCATTERING STATES OF THE GROSS-PITAEVSKII EQUATION 67
5.1 INTRODUCTION 67
5.1.1 SCALING BEHAVIOR OF THE GROSS-PITAEVSKII EQUATION 68
5.1.2 THE POSITION DEPENDENT INTERACTION STRENGTH 69
5.2 NUMERICAL SOLUTION OF THE NON-LINEAR SYSTEM OF EQUATIONS 71
5.2.1 CALCULATION OF THE DERIVATIVE 72
5.2.2 SELECTION OF THE START VECTOR 73
5.3 THE CURVE TRACKING ALGORITHM 76
5.3.1 CALCULATION OF THE TANGENT VECTOR 77
5.3.2 CRITICAL POINTS 78
5.3.3 ADAPTIVE STEPSIZE CONTROL 81
5.3.4 ARTIFICIAL HOMOTOPY 82
5.4 TIME DEPENDENT SIMULATIONS . . 83
5.4.1 TIME DEPENDENT POPULATION OF THE SCATTERING SYSTEM 83
5.4.2 TIME
DEPENDENT VARIATION
OF FI 85
5.4.3 TIME
DEPENDENT VARIATION
OF G
AND
J
IA
86
5.5 CURVE TRACKING FOR VARIOUS PARAMETERS 88
5.6 PERTURBATION THEORY 92
5.6.1 PERTURBATION THEORY FOR THE WAVE FUNCTION 92
5.6.2 PERTURBATION THEORY FOR THE ENERGY 94
5.7 DYNAMICAL STABILITY 100
5.8 OTHER GEOMETRIES 105
5.8.1 SS
2
: A NEARLY CLOSED SYSTEM WITHOUT HORIZONTAL MIRROR SYMMETRY 105
5.8.2 BZ- A NEARLY CLOSED SYSTEM WITHOUT ANY SYMMETRY 108
5.8.3 SS
4
: ANOTHER NEARLY CLOSED FUELL SYMMETRIE SYSTEM 108
5.8.4 B^: A WIDE OPEN SYSTEM WITH CLASSICAL CHAOTIC DYNAMICS 113
5.9 ONE DIMENSIONAL SYSTEMS WITH NON-TRIVIAL TOPOLOGY 118
5.9.1 SSSS .
A RING WITH VANISHING POTENTIAL 119
5.9.2
BF.
A RING WITH A WEAK DISORDER POTENTIAL 122
5.9.3 BS: A RING WITH A STRONG DISORDER POTENTIAL 122
5.10 SUMMARY 122
CONTENTS VII
6 SCATTERING STATES IN CHAOTIC BILLIARDS 125
6.1 WEAK LOCALIZATION 126
6.1.1 WEAK LOCALIZATION IN THE LINEAR REGIME 126
6.1.2 WEAK LOCALIZATION IN THE NON-LINEAR REGIME 132
6.1.3 ANALYSIS OF THE CLASSICAL DYNAMICS 136
6.1.4 COMPARISON WITH NUMERICAL RESULTS 141
6.1.5 DIRECT EVALUATION OF THE SEMICLASSICAL SUM 147
6.2 INTENSITY DISTRIBUTION 150
6.2.1 THEORETICAL ANALYSIS 150
6.2.2 COMPARISON WITH NUMERICAL RESULTS 154
6.3 OTHER GEOMETRIES 157
6.3.1 BG: THE CLIPPED TRIANGLE 157
6.3.2 BIO. THE STOMACH BILLIARD 157
6.3.3 BU . THE HALF CIRCLE (NARROW LEADS) 158
6.3.4 B 2- THE HALF CIRCLE (WIDE LEADS) 158
6.3.5 BI3: THE LIMAGON (NARROW LEADS) 158
6.3.6 B 4. THE LIMA^ON (WIDE LEADS) 158
6.4 RELATED EFFECTS IN MESOSCOPIC SYSTEMS 172
6.4.1 COHERENT BACKSCATTERING IN DISORDERED POTENTIALS 172
6.4.2 TIME-REVERSAL MIRRORS IN CHAOTIC CAVITIES 173
6.4.3 HALF-PERIOD AHARONOV-BOHM OSCILLATIONS IN DISORDERED RINGS 174
6.5 SUMMARY AND OUTLOOK 175
APPENDIX 177
A THE NEWTON METHOD 177
B THE ONSAGER RELATIONS 180
B.L SYMMETRIES OF THE SCATTERING MATRIX 180
B.2 THE ONSAGER RELATIONS 183
B.3 THE BREAKDOWN OF THE ONSAGER RELATIONS IN THE INTERACTING CASE 184
B.4 THE GENERALIZED CONTINUITY EQUATION 185
C TRANSPARENT BOUNDARY CONDITIONS 187
D BLOCK GAUSS MATRIX INVERSION 191
THE DYSON EQUATION 192
F
F DERIVATION OF THE PEIERLS PHASE 194
G THE STABILITY AMPLITUDE IN BIRKHOFF COORDINATES 197
H A SMOOTH SWITCHING FUNCTION 199
REFERENCES 204
|
| any_adam_object | 1 |
| author | Hartmann, Timo |
| author_facet | Hartmann, Timo |
| author_role | aut |
| author_sort | Hartmann, Timo |
| author_variant | t h th |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
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| discipline | Physik |
| edition | 1. Aufl. |
| format | Thesis Book |
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| indexdate | 2024-07-10T01:23:51Z |
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| physical | VII, 217 S. graph. Darst. |
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| publishDate | 2015 |
| publishDateSearch | 2015 |
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| publisher | Univ.-Verl. |
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| spelling | Hartmann, Timo Verfasser aut Transport of Bose-Einstein condensates through two dimensional cavities Timo Hartmann 1. Aufl. Regensburg Univ.-Verl. 2015 VII, 217 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dissertationsreihe Physik 44 Zugl.: Regensburg, Univ., Diss., 2014 Dimension 2 (DE-588)4321721-7 gnd rswk-swf Hohlraumresonator (DE-588)4160446-5 gnd rswk-swf Bose-Gas (DE-588)4146392-4 gnd rswk-swf Mean-Field-Theorie (DE-588)4337622-8 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Bose-Gas (DE-588)4146392-4 s Hohlraumresonator (DE-588)4160446-5 s Dimension 2 (DE-588)4321721-7 s Mean-Field-Theorie (DE-588)4337622-8 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:355-epub-312262 Dissertationsreihe Physik 44 (DE-604)BV035566746 44 http://epub.uni-regensburg.de/31226/ Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-312262 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027950758&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hartmann, Timo Transport of Bose-Einstein condensates through two dimensional cavities Dissertationsreihe Physik Dimension 2 (DE-588)4321721-7 gnd Hohlraumresonator (DE-588)4160446-5 gnd Bose-Gas (DE-588)4146392-4 gnd Mean-Field-Theorie (DE-588)4337622-8 gnd |
| subject_GND | (DE-588)4321721-7 (DE-588)4160446-5 (DE-588)4146392-4 (DE-588)4337622-8 (DE-588)4113937-9 |
| title | Transport of Bose-Einstein condensates through two dimensional cavities |
| title_auth | Transport of Bose-Einstein condensates through two dimensional cavities |
| title_exact_search | Transport of Bose-Einstein condensates through two dimensional cavities |
| title_full | Transport of Bose-Einstein condensates through two dimensional cavities Timo Hartmann |
| title_fullStr | Transport of Bose-Einstein condensates through two dimensional cavities Timo Hartmann |
| title_full_unstemmed | Transport of Bose-Einstein condensates through two dimensional cavities Timo Hartmann |
| title_short | Transport of Bose-Einstein condensates through two dimensional cavities |
| title_sort | transport of bose einstein condensates through two dimensional cavities |
| topic | Dimension 2 (DE-588)4321721-7 gnd Hohlraumresonator (DE-588)4160446-5 gnd Bose-Gas (DE-588)4146392-4 gnd Mean-Field-Theorie (DE-588)4337622-8 gnd |
| topic_facet | Dimension 2 Hohlraumresonator Bose-Gas Mean-Field-Theorie Hochschulschrift |
| url | http://epub.uni-regensburg.de/31226/ https://nbn-resolving.org/urn:nbn:de:bvb:355-epub-312262 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027950758&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035566746 |
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