Fractional Statistics And Quantum Theory
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Fractional Statistics And Quantum Theory
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Author : Avinash Khare
language : en
Publisher: World Scientific
Release Date : 2005
Fractional Statistics And Quantum Theory written by Avinash Khare and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Science categories.
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
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Author : Alberto Lerda
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-11
Anyons written by Alberto Lerda and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-11 with Science categories.
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
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Author : Frank Wilczek
language : en
Publisher: World Scientific
Release Date : 1990
Fractional Statistics And Anyon Superconductivity written by Frank Wilczek and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Technology & Engineering categories.
Part I: Concepts in fractional statistics, part II: States of anyon matter, part III: Reprinted papers
Fractional Quantum Mechanics
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Author : Laskin Nick
language : en
Publisher: World Scientific
Release Date : 2018-05-25
Fractional Quantum Mechanics written by Laskin Nick and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-25 with Science categories.
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
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Author : Lucjan Jacak
language : en
Publisher:
Release Date : 2003
Quantum Hall Systems written by Lucjan Jacak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Quantum Hall effect categories.
This text presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It covers the fundamental problems of two-dimensional quantum statistics in terms of topology and the Chern-Simons theory.
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets 5th Edition
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Author : Kleinert Hagen
language : en
Publisher: World Scientific
Release Date : 2009-05-18
Path Integrals In Quantum Mechanics Statistics Polymer Physics And Financial Markets 5th Edition written by Kleinert Hagen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-18 with Science categories.
This is the fifth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's time-sliced formula to include singular attractive 1/r- and 1/r2-potentials. The second is a new nonholonomic mapping principle carrying physical laws in flat spacetime to spacetimes with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations.In addition to the time-sliced definition, the author gives a perturbative, coordinate-independent definition of path integrals, which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely products of distributions.The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent results. The convergence is uniform from weak to strong couplings, opening a way to precise evaluations of analytically unsolvable path integrals in the strong-coupling regime where they describe critical phenomena.Tunneling processes are treated in detail, with applications to the lifetimes of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A variational treatment extends the range of validity to small barriers. A corresponding extension of the large-order perturbation theory now also applies to small orders.Special attention is devoted to path integrals with topological restrictions needed to understand 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, recently experienced in the world markets, that large fluctuations occur much more frequently than in Gaussian distributions.
Quantum Many Body Systems In One Dimension
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Author : Zachary N C Ha
language : en
Publisher: World Scientific
Release Date : 1996-09-13
Quantum Many Body Systems In One Dimension written by Zachary N C Ha and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-13 with Science categories.
The main theme of the book is the intimate connection between the two families of exactly solvable models: the inverse-square exchange (ISE) and the nearest-neighbor exchange (NNE) models. The latter are better known as the Bethe-Ansatz solvable models and include the Heisenberg spin chain, t–J models and Hubbard models. The former, the Calogero–Sutherland family of models, are simple to solve and contain essentially the same physics as the NNE family. The author introduces and discusses current topics, such as the Luttinger liquid concept, fractional statistics, and spin–charge separation, in the context of the explicit models. Contents:IntroductionHeisenberg Spin ChainThe 1D Hubbard ModelModels with Inverse-Square ExchangeStrings in Long-Range Interaction ModelElementary Excitations of t-J ModelFractional Statistics in One-Dimension: View from an Exactly Solvable ModelConcluding Remarks Readership: Graduate students, researchers in statistical mechanics, mathematical physics and condensed matter physics. keywords:Quantum;Many-Body;One;Inverse Square;Exchange;Luttinger;Fractional Statistics
The Quantum Hall Effect
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Author : Daijiro Yoshioka
language : en
Publisher:
Release Date : 2014-01-15
The Quantum Hall Effect written by Daijiro Yoshioka and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
The Role Of Topology In Classical And Quantum Physics
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Author : Giuseppe Morandi
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-11
The Role Of Topology In Classical And Quantum Physics written by Giuseppe Morandi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-11 with Science categories.
In solid-state physics especially topological techniques have turned out to be extremely useful for modelling and explaining physical properties of matter. This book illustrates various applications of algebraic topology in classical field theory (non-linear sigma-models) and in quantizationsin multiply connected spaces (anyons). It treats Chern-Simon Lagrangians, Berry's phase, the polarization of light and the fractional quantum Hall effect.
Quantum Hall Systems
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Author : Lucjan Jacak
language : en
Publisher: Oxford University Press, USA
Release Date : 2003
Quantum Hall Systems written by Lucjan Jacak and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This book presents cutting-edge topics in modern theoretical physics-quantum Hall systems-the subject of two Nobel Prizes in 1985 and 1998.