Spectral properties of magnetic edge states:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
2001
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | München, Univ., Fak. für Physik, Diss., 2001 |
| Beschreibung: | VIII, 173 S. Ill., graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
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CONTENTS
1 INTRODUCTION 1
1.1 FRAMEWORK. 1
1.2 FORMULATION OF THE PROBLEM AND OVERVIEW OF THE RESULTS. 2
1.3 STRUCTURE OF THE THESIS. 3
2 MOTION IN THE FREE MAGNETIC PLANE 5
2.1 CLASSICAL MOTION.
;-YYYYYYYY 5
2.2 QUANTIZATION. 7
2.3 THE SCALING PROPERTY. 11
2.4 THE FREE QUANTUM PROPAGATOR. 13
2.5 THE FREE GREEN FUNCTION. 15
2.5.1 THE SEMICLASSICAL GREEN FUNCTION. 16
2.5.2 THE EXACT GREEN FUNCTION. 18
2.5.3 PROPERTIES OF THE FREE GREEN FUNCTION. 19
NOTES. 21
3 INTRODUCING A BOUNDARY 23
3.1 MOTION IN A RESTRICTED DOMAIN. 23
3.2 THE CLASSICAL BILLIARD. 25
3.2.1 THE BILLIARD BOUNCE MAP. 25
3.2.2 INTEGRABLE AND HYPERBOLIC BILLIARDS. 26
3.2.3 THE INTERIOR-EXTERIOR DUALITY. 28
3.3 QUANTUM BILLIARDS. 30
3.3.1 GENERAL BOUNDARY CONDITIONS. 30
3.3.2 THE QUANTUM SPECTRUM. 31
3.3.3 ASYMPTOTIC COUNTING FUNCTIONS. 32
3.4 ORBITAL MAGNETISM . 35
4 QUANTIZATION IN THE INTERIOR AND THE EXTERIOR 39
4.1 BOUNDARY METHODS. 39
4.2 THE BOUNDARY INTEGRAL EQUATIONS. 40
4.2.1 SINGLE AND DOUBLE LAYER EQUATIONS. 40
4.2.2 SPURIOUS SOLUTIONS AND THE COMBINED OPERATOR. 43
4.2.3 WAVE FUNCTIONS. 45
4.3 THE BOUNDARY OPERATORS. 45
4.3.1 EXPLICIT EXPRESSION FOR THE INTEGRAL KERNELS. 45
4.3.2 THE HYPERSINGULAR INTEGRAL OPERATOR. 47
V
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/962141496
4.4 SOLVING THE INTEGRAL EQUATIONS . 48
4.5 NUMERICAL ANALYSIS. 51
5 RESULTS OF THE BOUNDARY INTEGRAL METHOD 55
5.1 SPECTRAL STATISTICS. 55
5.2 WAVE FUNCTIONS IN THE INTERIOR AND IN THE EXTERIOR. 58
5.3 GENERAL BOUNDARY CONDITIONS. 64
6 SEMICLASSICAL QUANTIZATION 69
6.1 THE SEMICLASSICAL BOUNDARY INTEGRAL OPERATORS. 70
6.2 FROM BOUNDARY TO MAP OPERATORS. 73
6.3 TRACE FORMULA FOR HYPERBOLIC BILLIARDS. 76
6.3.1 THE SADDLE POINT CONDITIONS. 76
6.3.2 THE PREFACTORS . 80
6.3.3 PERFORMING THE TRACE. 82
6.3.4 GEOMETRIC INTERPRETATION. 85
6.4 TRACE FORMULA FOR THE INTEGRABLE CASE. 87
6.4.1 THE DISK BILLIARD. 87
6.4.2 OPERATORS FOR THE INTEGRABLE MAP. 88
6.4.3 THE EXPLICIT TRACE FORMULA. 89
NOTES. 92
7 SEPARABLE GEOMETRIES 93
7.1 THE DISK BILLIARD. 93
7.1.1 SEMICLASSICAL QUANTIZATION.
94
7.1.2 RELATION TO THE PERIODIC ORBIT FORMULA.
96
7.1.3 EXACT QUANTIZATION. 99
7.2 THE PERIODIC LINE. 100
*
8 A SPECTRAL MEASURE FOR EDGE STATES 105
8.1 BULK STATES AND EDGE STATES. 105
8.1.1 A QUANTUM CRITERION. 105
8.1.2 THE DENSITY OF EDGE STATES. 106
8.2 THE SEMICLASSICAL DENSITY OF EDGE STATES.109
8.3 ASYMPTOTIC PROPERTIES OF EDGE AND BULK STATES. 112
8.3.1 BULK STATE ENERGIES AND WEIGHTS. 112
8.3.2 THE MEAN EDGE COUNTING FUNCTION. 115
8.4 EDGE MAGNETIZATION AS A SPECTRAL MEASURE. 115
9 PROPERTIES OF EDGE STATE SPECTRA 119
9.1 UNIVERSAL AUTO-CORRELATIONS. 119
9.2 THE ACTION SPECTRUM. 123
9.3 USING THE EDGE MAGNETIZATION.125
VI
10 SPECTRAL CROSS CORRELATIONS 129
10.1 THE PREDICTION OF SPECTRAL CROSS CORRELATIONS. 129
10.2 STATISTICAL EVIDENCE. 132
10.3 THE PAIR RELATION. 136
10.4 CONCLUSIONS.143
APPENDICES 145
A MATHEMATICAL APPENDIX 145
A.L THE STATIONARY PHASE APPROXIMATION. 145
A. 2 THE SINGULAR INTEGRALS. 146
B ANGULAR MOMENTUM REPRESENTATION 148
B. L FREE GREEN FUNCTION. 148
B.2 THE NULL FIELD METHOD.150
C THE PRODUCT RELATION OF THE MAP OPERATORS 152
D SCALED SPECTRA 154
E NUMERICAL EVALUATION OF THE GREEN FUNCTION 155
LIST OF SYMBOLS 159
BIBLIOGRAPHY 165
VII |
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| indexdate | 2024-10-09T18:07:48Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009471477 |
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| physical | VIII, 173 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
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| spelling | Hornberger, Klaus 1971- Verfasser (DE-588)123097622 aut Spectral properties of magnetic edge states von Klaus Hornberger 2001 VIII, 173 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Univ., Fak. für Physik, Diss., 2001 Hochschulschrift gtt Randintegral (DE-588)4607681-5 gnd rswk-swf Billard Mathematik (DE-588)4605041-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Billard Mathematik (DE-588)4605041-3 s Randintegral (DE-588)4607681-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009471477&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hornberger, Klaus 1971- Spectral properties of magnetic edge states Hochschulschrift gtt Randintegral (DE-588)4607681-5 gnd Billard Mathematik (DE-588)4605041-3 gnd |
| subject_GND | (DE-588)4607681-5 (DE-588)4605041-3 (DE-588)4113937-9 |
| title | Spectral properties of magnetic edge states |
| title_auth | Spectral properties of magnetic edge states |
| title_exact_search | Spectral properties of magnetic edge states |
| title_full | Spectral properties of magnetic edge states von Klaus Hornberger |
| title_fullStr | Spectral properties of magnetic edge states von Klaus Hornberger |
| title_full_unstemmed | Spectral properties of magnetic edge states von Klaus Hornberger |
| title_short | Spectral properties of magnetic edge states |
| title_sort | spectral properties of magnetic edge states |
| topic | Hochschulschrift gtt Randintegral (DE-588)4607681-5 gnd Billard Mathematik (DE-588)4605041-3 gnd |
| topic_facet | Hochschulschrift Randintegral Billard Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009471477&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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