Quantum Hall systems: braid groups, composite fermions, and fractional charge
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2003
|
| Edition: | 1. publ. |
| Series: | International series of monographs on physics
119 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 145 S. graph. Darst. |
| ISBN: | 0198528701 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
1
Introduction
Topological
methods for description of quantum many-body
systems
¡
;j
2.1
Configuration spaces of quantum many-body
systems of various dimensions
13
2.1.1
Configuration space of a many-particle system in
Euclidean space
14
2.2
Quantization of many-body systems Hi
2.3
The first homotopy group for the many-particle
configuration space -braid groups ¡H
2.4
Braid groups for specific manifolds
20
2.4.1
Full braid group for the Euclidean space R2
20
2.4.2
Full braid group for the sphere S2
24
2.4.3
Full braid group for the torus
Г 2Л
2.4.4
The full braid group for the three-dimensional
Euclidean space
1Ѓ
28
2.4.5
Braid groups for the line R1 and the circle
5 28
Quantization of many-particle systems and quantum
statistics in lower dimensions
30
3.1
Topological limitations of quantum-mechanical
description of many-particle systems
30
3.2
Quantum statistics and irreducible unitary representations of
braid groups for selected manifolds
31
3.2.1
Scalar quantum statistics of particles on the plane R2
31
3.2.2
Scalar statistics of particles on the sphere S2
32
3.2.3
Scalar statistics of particles on the torus
Τ
32
3.2.4
Scalar quantum statistics in three-dimensional Euclidean
space
Й3
33
3.2.5
Relation between spin and statistics
34
3.2.6
Aharonov-Bohm effect
35
3.2.7
Fractional statistics in one-dimensional system
37
3.3
Νοη
-Abełian
statistics
38
3.3.1
Projective
permutation statistics
39
Topological approach to composite
particles in two dimensions
41
4.1
Mathematical model of composite particles
41
4.1.1
Factor groups
x
CONTENTS
4.1.2
Group
Ω^
44
4.1.3
One-dimensional unitary representations of the group
Ω^
45
4.2
Configuration space for the system of composite particles
47
4.2.1
Configuration space for. two looped particles
47
4.2.2
Configuration space of the system of three looped
particles of the third order
49
5
Many-body methods for Chern-Simons systems
54
5.1
Random phase approximation for an anyon gas
54
5.2
Correlation energy of an anyon gas
59
5.3
Hartree-Fock approximation for Chern-Simons systems
62
5.4
Diagram analysis for a gas of anyons
65
5.4.1
Self-consistent
Hartree
approximation for a gas of anyons
65
5.4.2
Self-consistent Hartree-Fock approximation for gas of
anyons
69
6
Anyon superconductivity
71
6.1
Meissner effect in an anyon gas at
Τ
= 0 71
6.2
Gas of anyons at finite temperatures
75
6.3
Higgs mechanism in an anyon superconductor
77
6.4
Ground state of an anyon superconductor in the
Hartree—
Fock
approximation
81
7
The fractional quantum Hall effect in composite fermion
systems
83
7.1
Hall conductivity in a system of composite
fermions
83
7.2
Ground-state energy of composite fermion systems
88
7.3
Metal of composite
fermions
91
7.4
BCS (Bardeen-Cooper--Schrieffer) paired Hall state
93
8
Quantum Hall systems on a sphere
97
8.1
Spherical system
97
8.2
Composite fermion transformation
101
8.3
Hierarchy
105
9
Pseudopotential approach to the fractional quantum Hall
states 111
9.1
Problems with justification of the composite fermion picture 111
9.2
Numerical studies on the Haldane sphere
112
9.3
Pseudopotential approach
114
9.4
Energy spectra of short-range
pseudopotent
ials
116
9.5
Definition of short-range pseudopotential
119
9.6
Application to various pseudopotentials
120
9.7
Multi-component systems
124
CONTENTS xi
A
Homotopy
groups
130
В
Correlation function for an anyon gas in the self-consistent
Hartree
approximation
133
References
137
Index
143
|
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| id | DE-604.BV017966249 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:23:40Z |
| institution | BVB |
| isbn | 0198528701 |
| language | English |
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| physical | XI, 145 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | International series of monographs on physics |
| series2 | International series of monographs on physics |
| spelling | Quantum Hall systems braid groups, composite fermions, and fractional charge Lucjan Jacak ... 1. publ. Oxford Oxford Univ. Press 2003 XI, 145 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series of monographs on physics 119 Efeito hall larpcal Effet Hall quantique Quantum Hall effect Quanten-Hall-Effekt (DE-588)4124013-3 gnd rswk-swf Quanten-Hall-Effekt (DE-588)4124013-3 s DE-604 Jacak, Lucjan 1952- Sonstige (DE-588)115764127 oth International series of monographs on physics 119 (DE-604)BV000106406 119 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010765294&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Quantum Hall systems braid groups, composite fermions, and fractional charge International series of monographs on physics Efeito hall larpcal Effet Hall quantique Quantum Hall effect Quanten-Hall-Effekt (DE-588)4124013-3 gnd |
| subject_GND | (DE-588)4124013-3 |
| title | Quantum Hall systems braid groups, composite fermions, and fractional charge |
| title_auth | Quantum Hall systems braid groups, composite fermions, and fractional charge |
| title_exact_search | Quantum Hall systems braid groups, composite fermions, and fractional charge |
| title_full | Quantum Hall systems braid groups, composite fermions, and fractional charge Lucjan Jacak ... |
| title_fullStr | Quantum Hall systems braid groups, composite fermions, and fractional charge Lucjan Jacak ... |
| title_full_unstemmed | Quantum Hall systems braid groups, composite fermions, and fractional charge Lucjan Jacak ... |
| title_short | Quantum Hall systems |
| title_sort | quantum hall systems braid groups composite fermions and fractional charge |
| title_sub | braid groups, composite fermions, and fractional charge |
| topic | Efeito hall larpcal Effet Hall quantique Quantum Hall effect Quanten-Hall-Effekt (DE-588)4124013-3 gnd |
| topic_facet | Efeito hall Effet Hall quantique Quantum Hall effect Quanten-Hall-Effekt |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010765294&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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