Quantum Hall systems : braid groups, composite fermions, and fractional charge /
Saved in:
| Imprint: | Oxford ; New York : Oxford University Press, c2003. |
|---|---|
| Description: | xi, 145 p. : ill. ; 24 cm. |
| Language: | English |
| Series: | International series of monographs on physics ; no. 119 |
| Subject: | |
| Format: | E-Resource Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5082002 |
Table of Contents:
- 1. Introduction
- 2. Topological methods for description of quantum many-body systems
- 2.1. Configuration spaces of quantum many-body systems of various dimensions
- 2.1.1. Configuration space of a many-particle system in Euclidean space
- 2.2. Quantization of many-body systems
- 2.3. The first homotopy group for the many-particle configuration space--braid groups
- 2.4. Braid groups for specific manifolds
- 2.4.1. Full braid group for the Euclidean space R[superscript 2]
- 2.4.2. Full braid group for the sphere S[superscript 2]
- 2.4.3. Full braid group for the torus T
- 2.4.4. The full braid group for the three-dimensional Euclidean space R[superscript 3]
- 2.4.5. Braid groups for the line R[superscript 1] and the circle S[superscript 1]
- 3. Quantization of many-particle systems and quantum statistics in lower dimensions
- 3.1. Topological limitations of quantum-mechanical description of many-particle systems
- 3.2. Quantum statistics and irreducible unitary representations of braid groups for selected manifolds
- 3.2.1. Scalar quantum statistics of particles on the plane R[superscript 2]
- 3.2.2. Scalar statistics of particles on the sphere S[superscript 2]
- 3.2.3. Scalar statistics of particles on the torus T
- 3.2.4. Scalar quantum statistics in three-dimensional Euclidean space R[superscript 3]
- 3.2.5. Relation between spin and statistics
- 3.2.6. Aharonov-Bohm effect
- 3.2.7. Fractional statistics in one-dimensional system
- 3.3. Non-Abelian statistics
- 3.3.1. Projective permutation statistics
- 4. Topological approach to composite particles in two dimensions
- 4.1. Mathematical model of composite particles
- 4.1.1. Factor groups B[subscript N]/[Omega superscript n subscript N]
- 4.1.2. Group [Omega superscript n subscript N]
- 4.1.3. One-dimensional unitary representations of the group [Omega superscript n subscript N]
- 4.2. Configuration space for the system of composite particles
- 4.2.1. Configuration space for two looped particles
- 4.2.2. Configuration space of the system of three looped particles of the third order
- 5. Many-body methods for Chern-Simons systems
- 5.1. Random phase approximation for an anyon gas
- 5.2. Correlation energy of an anyon gas
- 5.3. Hartree-Fock approximation for Chern-Simons systems
- 5.4. Diagram analysis for a gas of anyons
- 5.4.1. Self-consistent Hartree approximation for a gas of anyons
- 5.4.2. Self-consistent Hartree-Fock approximation for gas of anyons
- 6. Anyon superconductivity
- 6.1. Meissner effect in an anyon gas at T = 0
- 6.2. Gas of anyons at finite temperatures
- 6.3. Higgs mechanism in an anyon superconductor
- 6.4. Ground state of an anyon superconductor in the Hartree-Fock approximation
- 7. The fractional quantum Hall effect in composite fermion systems
- 7.1. Hall conductivity in a system of composite fermions
- 7.2. Ground-state energy of composite fermion systems
- 7.3. Metal of composite fermions
- 7.4. BCS (Bardeen-Cooper-Schrieffer) paired Hall state
- 8. Quantum Hall systems on a sphere
- 8.1. Spherical system
- 8.2. Composite fermion transformation
- 8.3. Hierarchy
- 9. Pseudopotential approach to the fractional quantum Hall states
- 9.1. Problems with justification of the composite fermion picture
- 9.2. Numerical studies on the Haldane sphere
- 9.3. Pseudopotential approach
- 9.4. Energy spectra of short-range pseudopotentials
- 9.5. Definition of short-range pseudopotential
- 9.6. Application to various pseudopotentials
- 9.7. Multi-component systems
- A. Homotopy groups
- B. Correlation function for an anyon gas in the self-consistent Hartree approximation
- References
- Index
