Magnetic vortices in gauge/gravity duality:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2014
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| Schlagworte: | |
| Online-Zugang: | kostenfrei http://d-nb.info/1055907580/34 Inhaltsverzeichnis |
| Beschreibung: | XI, 161 S. Ill., graph. Darst. |
Internformat
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Datensatz im Suchindex
| _version_ | 1804152529391452160 |
|---|---|
| adam_text | MAGNETIC
VORTICES
IN GAUGE/GRAVITY
DUALITY
DISSERTATION
AN DER FAKULTAT FUR PHYSIK
DER LUDWIG-MAXIMILIANS-UNIVERSITAT
MIINCHEN
VORGELEGT VON
MIGAEL STRYDOM
AUS PRETORIA
MIINCHEN, DEN 20. MAI 2014
HTTP://D-NB.INFO/1055055037
CONTENTS
1 INTRODUCTION 1
2 GAUGE/GRAVITY DUALITY 13
2.1 THE ORIGINAL ADS/CFT CORRESPONDENCE 15
2.1.1 THE OPEN STRING PICTURE 16
2.1.2 THE CLOSED STRING PICTURE 17
2.1.3 MALDACENA S CONJECTURE 18
2.1.4 MATCHING SYMMETRIES 20
2.2 PRACTICALITIES 21
2.2.1 EXAMPLE WITH A GAUGE FIELD 21
2.2.2 MORE GENERAL OPERATORS 23
2.3 EXTENSIONS 24
2.3.1 FINITE TEMPERATURE IN FIELD THEORY AND CHEMICAL POTENTIALS . 26
2.3.2 BLACK HOLES AND THERMAL FIELD THEORIES 29
2.4 SUMMARY 31
3 MAGNETIC VORTEX LINES 33
3.1 GINZBURG-LANDAU EFFECTIVE FIELD THEORY MODEL 33
3.2 THE NIELSEN-OLESEN VORTEX 35
3.3 A VORTEX LATTICE IN TYPE-II SUPERCONDUCTORS 38
3.4 QUANTUM CHROMODYNAMICS AND STRONG MAGNETIC FIELDS 40
3.4.1 SU{2) YANG-MILLS 40
3.4.2 THE DSGS MODEL 42
4 HOLOGRAPHIC SUPERCONDUCTORS 45
4.1 A HOLOGRAPHIC 5-WAVE SUPERCONDUCTOR 46
4.1.1 THE OPTICAL CONDUCTIVITY 50
4.2 A HOLOGRAPHIC 7?-WAVE SUPERCONDUCTOR 53
4.3 INHOMOGENEOUS GROUND STATES 56
4.3.1 EXPLICIT SYMMETRY BREAKING 56
4.3.2 SPONTANEOUS SYMMETRY BREAKING 57
4.3.3 MAGNETIC FIELDS 59
5 HOLOGRAPHIC LATTICE GROUND STATES FROM A MAGNETIC FIELD 63
5.1 HOLOGRAPHIC SETUP 64
5.1.1 GEOMETRY 64
5.1.2 THE YANG-MILLS ACTION 65
5.1.3 READING OFF FIELD THEORY QUANTITIES 66
IX
X
CONTENTS
5.2 PERTURBATIVE STRATEGY 66
5.2.1 THE COMPARISON TO GINZBURG-LANDAU THEORY 67
5.2.2 THE GAUGE FIELD PERTURBATIVE EXPANSION 67
5.3 THE LINEARISED EQUATIONS 69
5.3.1 SEPARATING THE EQUATIONS 69
5.3.2 FLUCTUATION STABILITY ANALYSIS 73
5.3.3 THE POLES OF THE RETARDED GREEN S FUNCTION 74
5.3.4 SCHRODINGER POTENTIAL ANALYSIS 77
5.4 LATTICE SOLUTIONS 79
5.4.1 THE ABRIKOSOV LATTICE SOLUTION 80
5.5 THE GAUGE THEORY GROUND STATE ENERGY 81
5.6 SOLVING THE EQUATIONS TO HIGHER ORDERS 82
5.7 NUMERICAL SOLUTIONS 83
5.8 RESULTS 84
5.8.1 FINDING THE MINIMUM ENERGY STATE 84
5.9 AN ANALYSIS OF P = 2 SOLUTIONS 85
5.10 CONCLUSION 88
6 EXTENDING THE HOLOGRAPHIC LATTICE GROUND STATE MODEL 89
6.1 ADDING THE CHEMICAL POTENTIAL 89
6.1.1 THE ANSATZ 89
6.1.2 THE LINEAR ORDER EQUATIONS OF MOTION 90
6.1.3 RESULTS FROM FIRST ORDER 91
6.1.4 RESULTS FROM SECOND ORDER 93
6.1.5 RESULTS FROM THIRD ORDER 95
6.1.6 THE FREE ENERGY RESULTS 96
6.2 ADDING PROBE FERMIONS 97
6.2.1 HOLOGRAPHIC SETUP 98
6.2.2 SOLVING THE DIRAC EQUATION 101
6.2.3 OUTLOOK 105
7 THE HOLOGRAPHIC KONDO MODEL 107
7.1 INTRODUCTION TO THE KONDO MODEL 108
7.2 THE TOP-DOWN HOLOGRAPHIC KONDO MODEL 113
7.3 THE BOTTOM-UP HOLOGRAPHIC KONDO MODEL 114
7.3.1 HOLOGRAPHIC SETUP 115
7.3.2 THE KONDO COUPLING 117
7.3.3 SUPERCONDUCTIVITY 118
7.4 THE TIME-DEPENDENT KONDO MODEL IN THE PROBE SCALAR LIMIT .... 120
7.4.1 EQUATIONS IN EDDINGTON-FINKELSTEIN COORDINATES 121
7.4.2 SOLVING FOR THE SCALAR PROBE USING SEPARATION OF VARIABLES . . 122
7.4.3 SOLVING FOR THE SCALAR PROBE USING A TIME-MARCHING METHOD 123
7.5 TIME-DEPENDENCE WITH GAUGE FIELD BACKREACTION 126
7.6 CONCLUDING REMARKS 129
8 CONCLUSION 133
A LARGE N EXPANSION IN GAUGE THEORIES 139
CONTENTS XI
B VORTEX LATTICE SOLUTION TO HIGHER ORDERS 141
B.L DERIVING THE EQUATIONS FOR A%.
Y
141
B.2 DERIVING THE EQUATIONS FOR
C
XITL
, CY
N
143
B.3 CALCULATING THE ENERGY 144
C MATHEMATICA CODE: THE HOLOGRAPHIC KONDO MODEL 147
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| spelling | Strydom, Migael Verfasser aut Magnetic vortices in gauge/gravity duality von Migael Strydom 2014 XI, 161 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Univ., Diss., 2014 Mit einer Zssfassung in dt. Sprache (DE-588)4113937-9 Hochschulschrift gnd-content Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:19-172099 https://nbn-resolving.org/urn:nbn:de:bvb:19-172099 Resolving-System kostenfrei Volltext http://d-nb.info/1055907580/34 Langzeitarchivierung Nationalbibliothek DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027520253&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Strydom, Migael Magnetic vortices in gauge/gravity duality |
| subject_GND | (DE-588)4113937-9 |
| title | Magnetic vortices in gauge/gravity duality |
| title_auth | Magnetic vortices in gauge/gravity duality |
| title_exact_search | Magnetic vortices in gauge/gravity duality |
| title_full | Magnetic vortices in gauge/gravity duality von Migael Strydom |
| title_fullStr | Magnetic vortices in gauge/gravity duality von Migael Strydom |
| title_full_unstemmed | Magnetic vortices in gauge/gravity duality von Migael Strydom |
| title_short | Magnetic vortices in gauge/gravity duality |
| title_sort | magnetic vortices in gauge gravity duality |
| topic_facet | Hochschulschrift |
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