Fractional Statistics and Quantum Theory

Fractional Statistics and Quantum Theory
Author: Avinash Khare
Publisher: World Scientific
Total Pages: 316
Release: 2005
Genre: Science
ISBN: 9812561609

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.

Anyons

Anyons
Author: Alberto Lerda
Publisher: Springer Science & Business Media
Total Pages: 143
Release: 2008-09-11
Genre: Science
ISBN: 3540474668

Particles with fractional statistics interpolating between bosons and fermions have attracted considerable interest from mathematical physicists. In recent years it has emerged that these so-called anyons have rather unexpected applications, such as the fractional Hall effect, anyonic excitations in films of liquid helium, and high-temrperature superconductivity. Furthermore, they are discussed also in the context of conformal field theories. This book is a systematic and pedagogical introduction that considers the subject of anyons from many different points of view. In particular, the author presents the relation of anyons to braid groups and Chern-Simons field theory and devotes three chapters to physical applications. The book, while being of interest to researchers, primarily addresses advanced students of mathematics and physics.

Fractional Statistics and Anyon Superconductivity

Fractional Statistics and Anyon Superconductivity
Author: Frank Wilczek
Publisher: World Scientific
Total Pages: 462
Release: 1990
Genre: Technology & Engineering
ISBN: 9789810200497

Part I: Concepts in fractional statistics, part II: States of anyon matter, part III: Reprinted papers

Fractional Quantum Mechanics

Fractional Quantum Mechanics
Author: Nick Laskin
Publisher: World Scientific
Total Pages: 358
Release: 2018-05-28
Genre: Science
ISBN: 9813223812

Fractional quantum mechanics is a recently emerged and rapidly developing field of quantum physics.This is the first monograph on fundamentals and physical applications of fractional quantum mechanics, written by its founder.The fractional Schrödinger equation and the fractional path integral are new fundamental physical concepts introduced and elaborated in the book. The fractional Schrödinger equation is a manifestation of fractional quantum mechanics. The fractional path integral is a new mathematical tool based on integration over Lévy flights. The fractional path integral method enhances the well-known Feynman path integral framework.Related topics covered in the text include time fractional quantum mechanics, fractional statistical mechanics, fractional classical mechanics and the α-stable Lévy random process.The book is well-suited for theorists, pure and applied mathematicians, solid-state physicists, chemists, and others working with the Schrödinger equation, the path integral technique and applications of fractional calculus in various research areas. It is useful to skilled researchers as well as to graduate students looking for new ideas and advanced approaches.

Quantum Hall Systems

Quantum Hall Systems
Author: Lucjan Jacak
Publisher: Oxford University Press, USA
Total Pages: 164
Release: 2003
Genre: Mathematics
ISBN: 9780198528708

This book presents cutting-edge topics in modern theoretical physics-quantum Hall systems-the subject of two Nobel Prizes in 1985 and 1998.

Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets
Author: Hagen Kleinert
Publisher: World Scientific
Total Pages: 1626
Release: 2009
Genre: Business & Economics
ISBN: 9814273570

Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.

Advanced Quantum Mechanics

Advanced Quantum Mechanics
Author: Guangjiong Ni
Publisher:
Total Pages: 0
Release: 2002
Genre: Quantum theory
ISBN: 9781589490109

This book is based on lecture notes developed in last twenty-two years during which the authors have been teaching a core graduate course, Quantum Mechanics II, in Fudan University. It covers a very broad range of topics, presenting the state of the art in Quantum Mechanics. Discussions on some topics such as Levinson theorem, Casimir effect, the essence of special relativity, the interpretation of wave function, geometric phase, fractional statistics, and paradoxes in quantum mechanics, reflect to some extent the authors' own research results. The book is profound, practical, enlightening, and pleasantly readable. It is not only a very good textbook for students majoring in theoretical, experimental, or applied physics, but also a very useful reference for researchers as well.

Quantum Field Theory of Many-Body Systems

Quantum Field Theory of Many-Body Systems
Author: Xiao-Gang Wen
Publisher: OUP Oxford
Total Pages: 520
Release: 2004-06-04
Genre: Science
ISBN: 0191523968

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.

Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications

Non-perturbative Quantum Field Theory: Mathematical Aspects And Applications
Author: Jurg Frohlich
Publisher: World Scientific
Total Pages: 855
Release: 1992-04-29
Genre:
ISBN: 9814506567

Compiled to illustrate the recent history of Quantum Field Theory and its trends, this collection of selected reprints by Jürg Fröhlich, a leading theoretician in the field, is a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past fifteen years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature.The volume begins with a comprehensive introduction by Jürg Fröhlich.The theory of phase transitions and continuous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of λϖ4 — theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on “random geometry”. The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory.

The Quantum Hall Effect

The Quantum Hall Effect
Author: Richard E. Prange
Publisher: Springer Science & Business Media
Total Pages: 487
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 146123350X

After a foreword by Klaus von Klitzing, the first chapters of this book discuss the prehistory and the theoretical basis as well as the implications of the discovery of the Quantum Hall effect on superconductivity, superfluidity, and metrology, including experimentation. The second half of this volume is concerned with the theory of and experiments on the many body problem posed by fractional effect. Specific unsolved problems are mentioned throughout the book and a summary is made in the final chapter. The quantum Hall effect was discovered on about the hundredth anniversary of Hall's original work, and the finding was announced in 1980 by von Klitzing, Dorda and Pepper. Klaus von KIitzing was awarded the 1985 Nobel prize in physics for this discovery.