Holdings: Finite-size scaling for lattice fermions in two dimensions

Finite-size scaling for lattice fermions in two dimensions:

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Bibliographic Details
Main Author:	Hill, Antonio 1980- (Author)
Format:	Thesis Book
Language:	English
Published:	2012
Subjects:	Fermion Fermionensystem Skalierungsgesetz Gittermodell Numerisches Verfahren Übertragungsmatrix Hochschulschrift
Online Access:	Volltext https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-22679 Inhaltsverzeichnis
Physical Description:	XII, 106 S. Ill., graph. Darst.

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MARC


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Record in the Search Index

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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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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

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