Finite-size scaling for lattice fermions in two dimensions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2012
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-22679 Inhaltsverzeichnis |
| Beschreibung: | XII, 106 S. Ill., graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Finite-size scaling for lattice fermions in two dimensions |c vorgelegt von Antonio Hill |
| 264 | 1 | |c 2012 | |
| 300 | |a XII, 106 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a Augsburg, Univ., Diss., 2013 | ||
| 650 | 0 | 7 | |a Fermion |0 (DE-588)4121256-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Fermionensystem |0 (DE-588)4252865-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Skalierungsgesetz |0 (DE-588)4205012-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gittermodell |0 (DE-588)4226961-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Übertragungsmatrix |0 (DE-588)4137772-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Fermion |0 (DE-588)4121256-3 |D s |
| 689 | 0 | 1 | |a Fermionensystem |0 (DE-588)4252865-3 |D s |
| 689 | 0 | 2 | |a Gittermodell |0 (DE-588)4226961-1 |D s |
| 689 | 0 | 3 | |a Skalierungsgesetz |0 (DE-588)4205012-1 |D s |
| 689 | 0 | 4 | |a Übertragungsmatrix |0 (DE-588)4137772-2 |D s |
| 689 | 0 | 5 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
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| 912 | |a ebook | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-025989443 | ||
Datensatz im Suchindex
| _version_ | 1804150329791479808 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1. INTRODUCTION 5
2. DIRAC FERMIONS IN GRAPHENE 9
2.1. TIGHT-BINDING MODEL 9
2.1.1. BREAKING THE SUBLATTICE SYMMETRY AND GENERATING MASS ... 13
3. TRANSFER MATRIX APPROACH 15
3.1. APPLICATION TO DIRAC FERMIONS IN ONE DIMENSION 16
3.1.1. TRANSMISSION THROUGH A MASSIVE BARRIER 16
3.1.2. TRANSMISSION THROUGH N IDENTICAL BARRIERS 19
3.1.3. TRANSMISSION THROUGH A SCALAR POTENTIAL BARRIER 21
4. LYAPUNOV EXPONENT AND LOCALIZATION LENGTH 23
4.1. DEFINITION AND PROPERTIES 23
4.1.1. IDENTICAL NON-RANDOM MATRICES 24
4.2. NUMERICAL ALGORITHM 25
5. FINITE-SIZE SCALING 27
6. DIRAC EQUATION ON A LATTICE 31
6.1. DISCRETIZATION IN ONE DIMENSION 31
6.1.1. RECURRENCE EQUATION 33
6.1.2. CONSTRUCTING THE TRANSFER MATRIX 36
6.2. DISCRETIZATION IN TWO DIMENSIONS 41
6.2.1. SYMMETRIC DISCRETIZATION - MODEL A . . . 41
6.2.2. SIMPLIFIED MODEL A AND WEAK DISORDER EXPANSION 48
6.2.3. NON-SYMMETRIC DISCRETIZATION - MODEL B 57
6.2.4. COMPARISON OF MODEL A AND B WITHOUT DISORDER 60
7. LATTICE FERMIONS WITH RANDOM GAP: INFLUENCE OF VALLEY SYMMETRY BREAK
ING 65
7.1. MODEL A PRESERVED VALLEY SYMMETRY 65
7.2. MODEL A: BROKEN VALLEY SYMMETRY 67
7.2.1. CRITICAL EXPONENTS FOR THE METAL-INSULATOR TRANSITION 69
3
HTTP://D-NB.INFO/1038438330
IMAGE 2
CONTENTS
7.2.2. CRITICAL EXPONENT FOR THE INSULATOR-INSULATOR TRANSITION .... 74
7.2.3. PHASE DIAGRAM 74
7.3. MODEL B 76
7.3.1. CRITICAL EXPONENT FOR THE INSULATOR-INSULATOR TRANSITION .... 76
7.4. SUMMARY 78
8. LATTICE FERMIONS AND THE CHALKER-CODDINGTON MODEL 81
8.1. CHALKER-CODDINGTON NETWORK MODEL 81
8.2. MODEL A: BROKEN VALLEY SYMMETRY AND SCALAR DISORDER 85
8.2.1. FINITE-SIZE SCALING FOR THE DISORDER DEPENDENCE 85
8.2.2. FINITE-SIZE SCALING FOR THE ENERGY DEPENDENCE 87
8.3. SUMMARY 88
9. TIGHT-BINDING MODELS.FOR LATTICE FERMIONS WITH RANDOM MASS 89 9.1.
BRICKWORK LATTICE 89
9.1.1. SCALING BEHAVIOR WITH STAGGERED POTENTIAL 91
9.2. SCALING BEHAVIOR FOR THE 7R-FLUX LATTICE 92
9.3. SUMMARY 94
10. CONCLUSION 95
APPENDIX 96
A. PROBABILITY DENSITIES 97
B. TRANSFER MATRIX FOR THE CHALKER-CODDINGTON MODEL 99
BIBLIOGRAPHY 101
4
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| any_adam_object | 1 |
| author | Hill, Antonio 1980- |
| author_GND | (DE-588)103476120X |
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| author_sort | Hill, Antonio 1980- |
| author_variant | a h ah |
| building | Verbundindex |
| bvnumber | BV041011872 |
| classification_rvk | UL 4000 UP 3600 |
| collection | ebook |
| ctrlnum | (OCoLC)844111937 (DE-599)BVBBV041011872 |
| discipline | Physik |
| format | Thesis Book |
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| indexdate | 2024-07-10T00:37:12Z |
| institution | BVB |
| language | English |
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| physical | XII, 106 S. Ill., graph. Darst. |
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| spelling | Hill, Antonio 1980- Verfasser (DE-588)103476120X aut Finite-size scaling for lattice fermions in two dimensions vorgelegt von Antonio Hill 2012 XII, 106 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Augsburg, Univ., Diss., 2013 Fermion (DE-588)4121256-3 gnd rswk-swf Fermionensystem (DE-588)4252865-3 gnd rswk-swf Skalierungsgesetz (DE-588)4205012-1 gnd rswk-swf Gittermodell (DE-588)4226961-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Übertragungsmatrix (DE-588)4137772-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Fermion (DE-588)4121256-3 s Fermionensystem (DE-588)4252865-3 s Gittermodell (DE-588)4226961-1 s Skalierungsgesetz (DE-588)4205012-1 s Übertragungsmatrix (DE-588)4137772-2 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:384-opus4-22679 http://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/2267 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-22679 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025989443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hill, Antonio 1980- Finite-size scaling for lattice fermions in two dimensions Fermion (DE-588)4121256-3 gnd Fermionensystem (DE-588)4252865-3 gnd Skalierungsgesetz (DE-588)4205012-1 gnd Gittermodell (DE-588)4226961-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Übertragungsmatrix (DE-588)4137772-2 gnd |
| subject_GND | (DE-588)4121256-3 (DE-588)4252865-3 (DE-588)4205012-1 (DE-588)4226961-1 (DE-588)4128130-5 (DE-588)4137772-2 (DE-588)4113937-9 |
| title | Finite-size scaling for lattice fermions in two dimensions |
| title_auth | Finite-size scaling for lattice fermions in two dimensions |
| title_exact_search | Finite-size scaling for lattice fermions in two dimensions |
| title_full | Finite-size scaling for lattice fermions in two dimensions vorgelegt von Antonio Hill |
| title_fullStr | Finite-size scaling for lattice fermions in two dimensions vorgelegt von Antonio Hill |
| title_full_unstemmed | Finite-size scaling for lattice fermions in two dimensions vorgelegt von Antonio Hill |
| title_short | Finite-size scaling for lattice fermions in two dimensions |
| title_sort | finite size scaling for lattice fermions in two dimensions |
| topic | Fermion (DE-588)4121256-3 gnd Fermionensystem (DE-588)4252865-3 gnd Skalierungsgesetz (DE-588)4205012-1 gnd Gittermodell (DE-588)4226961-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Übertragungsmatrix (DE-588)4137772-2 gnd |
| topic_facet | Fermion Fermionensystem Skalierungsgesetz Gittermodell Numerisches Verfahren Übertragungsmatrix Hochschulschrift |
| url | http://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/2267 https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-22679 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025989443&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hillantonio finitesizescalingforlatticefermionsintwodimensions |