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Fractional statistics and quantum theory

Author: Avinash Khare
Publisher: Singapore ; Hackensack, N.J. : World Scientific, ©2005.
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:
"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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Avinash Khare
ISBN: 9812561609 9789812561602
OCLC Number: 60708854
Description: xiii, 300 pages : illustrations ; 24 cm
Contents: Machine derived contents note: 1I. Introduction 1 --
i11 Historical Review 3 --
1-2 Plan of the Book 12 --
References 15 --
2. Fractional Statistics in Two Dimensions 19 --
2.1 Introduction 19 --
2.2 Why Fractional Spin? 20 --
2.3 Why Fractional Statistics? 21 --
2.4 Basic Properties of Anyons 29 --
2,5 Elux Tube Model of Anyons , 32 --
2.6 The Braid Group 38 --
R eferences 42 --
3. Quantum Mechanics of Anyons 43 --
3.1 Introduction 43 --
3.2 Two Noninteracting Anyons 44 --
3.,3 Two Anyons in an Oscillator Potential 47 --
3.4 Two Anyons in a Uniform Magnetic Field 51 --
3,5 Magnetic Field with Coulomb Repulsion 57 --
3.6 Scattering of Two Anyons in Coulomb Field 58 --
3. Scattering of Two Anyons with Hard-DEk Repulsion 62 --
3.8 N Anyons in an Oscillator Potential 65 --
3.9 Three-Anyon Ground State. 69, --
3.10 General Results for N Anyons --
3.1i N Anyone Experiencing a, N-body Potential 83 --
3.12 N.Anyous in a Uniform Magnetic Field 87 --
3.13 Pseudo-Integrability of N Anyon System '9 --
3.14 Quanturn Computing and Anyons 96 --
References 100 --
4. Statistical Mechanics of an Ideal Anyop Gas 103 --
4.1 Introduction 103 --
4.2 Ideal Fermi Gas in Two Dimensions , 104 --
U.3 Ideal Bose Gas in Two Dimensions 1 1o --
4.4 Ideal Anyon Gas: Second Virial Coefficient 115 --
4.5 Ideal Anyon Gas: Third Virial Coefficient 130 --
4.6 Ideal Anyon Gas: Higher Virial Coefficients 140 --
References , , 2 --
5. Fractional Exclusion Statistics 1 45 --
5.1 Introduction 145 --
52 Distribution Function 146 --
5.3 Thermodynamics of an Ideal Gas 150 --
54 Negative Probabilities. 157 --
5.5 Gentile Statistics , 1.59 --
5.6 New Fractional Exclusion Statistics 162 --
References 164 --
164 --
6. Introduction to the Chern-Simons Term 167 --
6-1 Introduction 16 67 --
6.2 What is the Chern-Simons Term? 168 --
6,3 Gauge Invariant Mass Term 170 --
64. Behavior Under C, P , and T 172. --
6.5 Coleman-i-ill Theorem 173 --
66 Magneto-Electric Effect 175 --
6,7 Chern-Simons Term by SSB1 1,75 --
6.8 Lorentz Invariance from Gauge Invariance 176 --
6.9 Quantization of Chern-Simons Mass 177 --
6.10 Parity Anomaly , , 181 --
6.11 Topological Field Theory 182 --
" "-: i::: :- .::: :ils- ? lO --
References 183 --
7 o Soliton as Anyon in Field Theories 185 --
7.1 introduction. 5 15 --
2 Charged Vortex Solutions 186 --
3 Relatvistic Cherm-Simons Vortices 197 --
T4 Non-relativistic Chern-Simons Vortices 08 --
7.5 CP' Soltons with HopfTerm. 213 --
References 217 --
8. Anyons as Elementary Field Quanta 221 --
1S Introduction ,. 221 --
8.2 Non-relativistic Field Theories 222 --
83 Relativistic Field Theories 231 --
References , ,,. 37 --
9. Anyon Superconductivity 239 --
901 Introduction 39 --
9,2 Mean Field Theory 242 --
9.3 The Random Phase Approxrmation 245 --
9.4 The Effective Lagrangian 249 --
9.5 Anyons and High-T, Superconductivity 251 --
9.6 Anyon Metal 253 --
References 254 --
10. Quantum. Hall Effect and Anions 257 --
10.1 Introduction , 257 --
10.2 The Landau Levels 9 2,59 --
10.3 Basics of Quantum Hall Effect 261 --
'0.4 Trial Wave Function and Anyous 264 --
10.5 Mean Field Theory 278 --
References 285 --
11. Omitted Topics 287 --
References 293 --
SJ [[ [ --
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Responsibility: Avinash Khare.
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Abstract:

"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.

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"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." Read more...

 
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