Fractional statistics and quantum theory
This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced researchers with a reasonable background in quantum and statisti...
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| Main Author | |
|---|---|
| Format | eBook Book |
| Language | English |
| Published |
Singapore
World Scientific Publishing Co. Pte. Ltd
2005
World Scientific World Scientific Publishing Company World Scientific Publishing |
| Edition | 2nd ed. |
| Subjects | |
| Online Access | Get full text |
| ISBN | 9789812561602 9789812567758 9812561609 9812567755 |
| DOI | 10.1142/2988 |
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| Abstract | This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced researchers with a reasonable background in quantum and statistical mechanics. Topics in the first part of the book include the flux tube model of anyons, the braid group and a detailed discussion about the various aspects of quantum and statistical mechanics of a noninteracting anyon gas. The second part of the book includes a detailed discussion about fractional statistics from the point of view of Chern-Simons theories. Topics covered here include Chern-Simons field theories, charged vortices, anyon superconductivity and the fractional quantum Hall effect. Since the publication of the first edition of the book, an exciting possibility has emerged, that of quantum computing using anyons. A section has therefore been included on this topic in the second edition. In addition, new sections have been added about scattering of anyons with hard disk repulsion as well as fractional exclusion statistics and negative probabilities. |
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| AbstractList | This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced researchers with a reasonable background in quantum and statistical mechanics.Topics in the first part of the book include the flux tube model of anyons, the braid group and a detailed discussion about the various aspects of quantum and statistical mechanics of a noninteracting anyon gas.The second part of the book includes a detailed discussion about fractional statistics from the point of view of Chern-Simons theories. Topics covered here include Chern-Simons field theories, charged vortices, anyon superconductivity and the fractional quantum Hall effect.Since the publication of the first edition of the book, an exciting possibility has emerged, that of quantum computing using anyons. A section has therefore been included on this topic in the second edition. In addition, new sections have been added about scattering of anyons with hard disk repulsion as well as fractional exclusion statistics and negative probabilities.Sample Chapter(s)Chapter 1: Introduction (676 KB)Contents:Fractional Statistics in Two DimensionsQuantum Mechanics of AnyonsStatistical Mechanics of an Ideal Anyon GasFractional Exclusion StatisticsIntroduction to the Chern-Simons TermSoliton as Anyon in Field TheoriesAnyons as Elementary Field QuantaAnyon SuperconductivityQuantum Hall Effect and AnyonsOmitted TopicsReadership: Condensed matter physicists, mathematical physicists and materials scientists. This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced researchers with a reasonable background in quantum and statistical mechanics. Topics in the first part of the book include the flux tube model of anyons, the braid group and a detailed discussion about the various aspects of quantum and statistical mechanics of a noninteracting anyon gas. The second part of the book includes a detailed discussion about fractional statistics from the point of view of Chern-Simons theories. Topics covered here include Chern-Simons field theories, charged vortices, anyon superconductivity and the fractional quantum Hall effect. Since the publication of the first edition of the book, an exciting possibility has emerged, that of quantum computing using anyons. A section has therefore been included on this topic in the second edition. In addition, new sections have been added about scattering of anyons with hard disk repulsion as well as fractional exclusion statistics and negative probabilities. |
| Author | Khare, Avinash |
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| Notes | Includes bibliographical references and index |
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| Snippet | This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at... |
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| SubjectTerms | Anyons Anyons -- Statistical methods Quantum statistics Quantum theory SCIENCE Statistical methods Statistique quantique Théorie quantique |
| SubjectTermsDisplay | Anyons Quantum statistics Quantum theory Statistique quantique Théorie quantique |
| TableOfContents | Fractional statistics and quantum theory -- Preface to the Second Edition -- Preface -- Contents -- Chapter 1: Introduction -- Chapter 2: Fractional Statistics in Two Dimensions -- Chapter 3: Quantum Mechanics of Anyons -- Chapter 4: Statistical Mechanics of an Ideal Anyon Gas -- Chapter 5: Fractional Exclusion Statistics -- Chapter 6: Introduction to the Chern-Simons Term -- Chapter 7: Soliton as Anyon in Field Theories -- Chapter 8: Anyons as Elementary Field Quanta -- Chapter 9: Anyon Superconductivity -- Chapter 10: Quantum Hall Effect and Anyons -- Chapter 11: Omitted Topics -- Index. Intro -- Preface to the Second Edition -- Preface -- Contents -- Chapter 1 Introduction -- 1.1 Historical Review -- 1.2 Plan of the Book -- References -- Chapter 2 Fractional Statistics in Two Dimensions -- 2.1 Introduction -- 2.2 Why Fractional Spin? -- 2.3 Why Fractional Statistics? -- Quantum Statistics in One Dimension -- 2.4 Basic Properties of Anyons -- 2.5 Flux Tube Model of Anyons -- Dynamical Realization of the Statistical Interaction -- Anyon Gauge vs. Magnetic Gauge -- 2.6 The Braid Group -- References -- Chapter 3 Quantum Mechanics of Anyons -- 3.1 Introduction -- 3.2 Two Noninteracting Anyons -- Two anyons in a circular box with hard walls -- 3.3 Two Anyons in an Oscillator Potential -- 3.4 Two Anyons in a Uniform Magnetic Field -- Two Anyons in Magnetic Field with Harmonic Attraction -- 3.5 Magnetic Field with Coulomb Repulsion -- 3.6 Scattering of Two Anyons in Coulomb Field -- 3.7 Scattering of Two Anyons with Hard-Disk Repulsion -- 3.8 N Anyons in an Oscillator Potential -- 3.9 Three-Anyon Ground State -- Radial Excitations -- 3.10 General Results for N Anyons -- 3.11 N Anyons Experiencing a N-body Potential -- 3.12 N Anyons in a Uniform Magnetic Field -- Three-Anyons in a Uniform Magnetic Field Plus an Oscillator Potential -- 3.13 Pseudo-Integrability of N Anyon System -- 3.14 Quantum Computing and Anyons -- References -- Chapter 4 Statistical Mechanics of an Ideal Anyon Gas -- 4.1 Introduction -- 4.2 Ideal Fermi Gas in Two Dimensions -- 4.3 Ideal Bose Gas in Two Dimensions -- 4.4 Ideal Anyon Gas: Second Virial Coefficient -- a2( ) using oscillator as a regulator -- a2( ) using Semi-classical Approximation -- Second Virial Coefficient for Anyons with Hard-disk Repulsion -- 4.5 Ideal Anyon Gas: Third Virial Coefficient -- Some Exact Results for a3( ) -- a3( ) within Semi-classical Approximation References -- Chapter 9 Anyon Superconductivity -- 9.1 Introduction -- 9.2 Mean Field Theory -- 9.3 The Random Phase Approximation -- 9.4 The Effective Lagrangian -- 9.5 Anyons and High-Tc Superconductivity -- 9.6 Anyon Metal -- References -- Chapter 10 Quantum Hall Effect and Anyons -- 10.1 Introduction -- 10.2 The Landau Levels -- 10.3 Basics of Quantum Hall Effect -- 10.4 Trial Wave Function and Anyons -- Laughlin's Trial Wave Function -- Analogy with classical plasma -- Computation of Charge -- Computation of Statistics -- Hierarchy Scheme -- 10.5 Mean Field Theory -- References -- Chapter 11 Omitted Topics -- References -- Index 4.6 Ideal Anyon Gas: Higher Virial Coefficients -- References -- Chapter 5 Fractional Exclusion Statistics -- 5.1 Introduction -- 5.2 Distribution Function -- 5.3 Thermodynamics of an Ideal Gas -- Constant Density of States -- Low Temperature and High Density -- High Temperature and Low Density -- Ideal Gas with D -- Low Density and High Temperature -- High density and low temperature -- General Remarks -- 5.4 Negative Probabilities -- 5.5 Gentile Statistics -- High Temperature, Low Density -- High Density, Low Temperature -- 5.6 New Fractional Exclusion Statistics -- High Temperature, Low Density -- References -- Chapter 6 Introduction to the Chern-Simons Term -- 6.1 Introduction -- 6.2 What is the Chern-Simons Term? -- 6.3 Gauge Invariant Mass Term -- 6.4 Behavior Under C, P, and T -- 6.5 Coleman-Hill Theorem -- 6.6 Magneto-Electric Effect -- 6.7 Chern-Simons Term by SSB -- 6.8 Lorentz Invariance from Gauge Invariance -- 6.9 Quantization of Chern-Simons Mass -- 6.10 Parity Anomaly -- 6.11 Topological Field Theory -- References -- Chapter 7 Soliton as Anyon in Field Theories -- 7.1 Introduction -- 7.2 Charged Vortex Solutions -- Unusual Higgs Mechanism -- Vortex-Vortex Interaction -- Fermion-Charged Vortex Interaction -- Non-abelian Charged Vortex Solutions -- 7.3 Relativistic Chern-Simons Vortices -- Topological Self-dual Solutions -- Non-topological Self-dual Solutions -- Interaction Between Self-Dual Chern-Simons Vortices -- Semi-Local Self-Dual Chern-Simons Vortices -- 7.4 Non-relativistic Chern-Simons Vortices -- Dynamical Symmetries of the Non-relativistic system -- 7.5 CP1 Solitons with Hopf Term -- References -- Chapter 8 Anyons as Elementary Field Quanta -- 8.1 Introduction -- 8.2 Non-relativistic Field Theories -- 8.3 Relativistic Field Theories -- Group Theory Aspects -- Wave Equation For Anyons -- Fundamental Fields as Anyons |
| Title | Fractional statistics and quantum theory |
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