"As an important feature, this book contains both mathematics and physics, properly balanced for a student interested in studying theoretical physics. There are many exercises to be worked out. I am pleased to highly recommend the book for any one interested in the anyons." Professor Mukunda P Das
The Australian National University
Reviews of the First "This lucid monograph is highly recommended for those who want to do further research in the area as well as for those who are merely curious about this unusual aspect of quantum many-body physics." Current Science "The overall style is clear and pedagogical, with emphasis on symmetry and simplicity ... I recommend this book for newcomers, graduate students and teachers who are interested in having an introduction to the topics of the book's title." Mathematical Reviews 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.

nexusstc/Fractional Statistics and Quantum Theory/161852800340099b06396578c9285f72.pdf

lgli/_394940.161852800340099b06396578c9285f72.pdf

lgrsnf/_394940.161852800340099b06396578c9285f72.pdf

zlib/Mathematics/Avinash Khare/Fractional Statistics And Quantum Theory, Second Edition_1103310.pdf

Universality In Nonequilibrium Lattice Systems: Theoretical Foundations Theoretical Foundations

Fractional Statistics And Quantum Theory (2nd Edition)

KHARE, AVINASH

World Scientific Publishing Co Pte Ltd

World Scientific Publishing Company, Singapore, 2005

2 edition, February 28, 2005

2nd Revised ed., FR, 2005

Singapore, Singapore

2, 20050202

2005 feb

до 2011-08

lg664374

{"edition":"2","isbns":["9789812561602","9789812567758","9812561609","9812567755"],"last_page":315,"publisher":"WORLD SCIENTIFIC"}

Preface to the Second Edition 8
Preface 10
Contents 12
Chapter 1 Introduction 16
1.1 Historical Review 18
1.2 Plan of the Book 27
References 30
Chapter 2 Fractional Statistics in Two Dimensions 34
2.1 Introduction 34
2.2 Why Fractional Spin? 35
2.3 Why Fractional Statistics? 36
Quantum Statistics in One Dimension 44
2.4 Basic Properties of Anyons 44
2.5 Flux Tube Model of Anyons 47
Dynamical Realization of the Statistical Interaction 49
Anyon Gauge vs. Magnetic Gauge 52
2.6 The Braid Group 53
References 57
Chapter 3 Quantum Mechanics of Anyons 58
3.1 Introduction 58
3.2 Two Noninteracting Anyons 59
Two anyons in a circular box with hard walls 61
3.3 Two Anyons in an Oscillator Potential 62
3.4 Two Anyons in a Uniform Magnetic Field 66
Two Anyons in Magnetic Field with Harmonic Attraction 70
3.5 Magnetic Field with Coulomb Repulsion 72
3.6 Scattering of Two Anyons in Coulomb Field 73
3.7 Scattering of Two Anyons with Hard-Disk Repulsion 77
3.8 N Anyons in an Oscillator Potential 80
3.9 Three-Anyon Ground State 84
Radial Excitations 85
3.10 General Results for N Anyons 92
3.11 N Anyons Experiencing a N-body Potential 98
3.12 N Anyons in a Uniform Magnetic Field 102
Three-Anyons in a Uniform Magnetic Field Plus an Oscillator Potential 104
3.13 Pseudo-Integrability of N Anyon System 110
3.14 Quantum Computing and Anyons 111
References 115
Chapter 4 Statistical Mechanics of an Ideal Anyon Gas 118
4.1 Introduction 118
4.2 Ideal Fermi Gas in Two Dimensions 119
4.3 Ideal Bose Gas in Two Dimensions 125
4.4 Ideal Anyon Gas: Second Virial Coefficient 130
a2( ) using oscillator as a regulator 133
a2( ) using Semi-classical Approximation 138
Second Virial Coefficient for Anyons with Hard-disk Repulsion 143
4.5 Ideal Anyon Gas: Third Virial Coefficient 145
Some Exact Results for a3( ) 148
a3( ) within Semi-classical Approximation 149
4.6 Ideal Anyon Gas: Higher Virial Coefficients 155
References 157
Chapter 5 Fractional Exclusion Statistics 160
5.1 Introduction 160
5.2 Distribution Function 161
5.3 Thermodynamics of an Ideal Gas 165
Constant Density of States 165
Low Temperature and High Density 166
High Temperature and Low Density 166
Ideal Gas with D 167
Low Density and High Temperature 168
High density and low temperature 169
General Remarks 171
5.4 Negative Probabilities 172
5.5 Gentile Statistics 174
High Temperature, Low Density 175
High Density, Low Temperature 176
5.6 New Fractional Exclusion Statistics 177
High Temperature, Low Density 178
References 179
Chapter 6 Introduction to the Chern-Simons Term 182
6.1 Introduction 182
6.2 What is the Chern-Simons Term? 183
6.3 Gauge Invariant Mass Term 185
6.4 Behavior Under C, P, and T 187
6.5 Coleman-Hill Theorem 188
6.6 Magneto-Electric Effect 190
6.7 Chern-Simons Term by SSB 190
6.8 Lorentz Invariance from Gauge Invariance 191
6.9 Quantization of Chern-Simons Mass 192
6.10 Parity Anomaly 196
6.11 Topological Field Theory 197
References 198
Chapter 7 Soliton as Anyon in Field Theories 200
7.1 Introduction 200
7.2 Charged Vortex Solutions 201
Unusual Higgs Mechanism 206
Vortex-Vortex Interaction 210
Fermion-Charged Vortex Interaction 211
Non-abelian Charged Vortex Solutions 211
7.3 Relativistic Chern-Simons Vortices 212
Topological Self-dual Solutions 215
Non-topological Self-dual Solutions 216
Interaction Between Self-Dual Chern-Simons Vortices 222
Semi-Local Self-Dual Chern-Simons Vortices 222
7.4 Non-relativistic Chern-Simons Vortices 223
Dynamical Symmetries of the Non-relativistic system 228
7.5 CP1 Solitons with Hopf Term 228
References 232
Chapter 8 Anyons as Elementary Field Quanta 236
8.1 Introduction 236
8.2 Non-relativistic Field Theories 237
8.3 Relativistic Field Theories 246
Group Theory Aspects 246
Wave Equation For Anyons 248
Fundamental Fields as Anyons 250
References 252
Chapter 9 Anyon Superconductivity 254
9.1 Introduction 254
9.2 Mean Field Theory 257
9.3 The Random Phase Approximation 260
9.4 The Effective Lagrangian 264
9.5 Anyons and High-Tc Superconductivity 266
9.6 Anyon Metal 268
References 269
Chapter 10 Quantum Hall Effect and Anyons 272
10.1 Introduction 272
10.2 The Landau Levels 274
10.3 Basics of Quantum Hall Effect 276
10.4 Trial Wave Function and Anyons 279
Laughlin’s Trial Wave Function 280
Analogy with classical plasma 281
Computation of Charge 285
Computation of Statistics 287
Hierarchy Scheme 289
10.5 Mean Field Theory 293
References 300
Chapter 11 Omitted Topics 302
References 308
Index 312
9812561609,9789812561602
World Scientific 2005

"This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. This is the only book on the subject covering almost all aspects of the field. 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." "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."--BOOK JACKET

2011-08-31