Fractional Quantum Mechanics

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Fractional Quantum Mechanics

Author : Laskin Nick
Publisher : World Scientific
ISBN 13 : 9813223812
Total Pages : 360 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Fractional Quantum Mechanics by : Laskin Nick

Download or read book Fractional Quantum Mechanics written by Laskin Nick and published by World Scientific. This book was released on 2018-05-25 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractional Statistics and Quantum Theory

Author : Avinash Khare
Publisher : World Scientific
ISBN 13 : 9812567755
Total Pages : 316 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Fractional Statistics and Quantum Theory by : Avinash Khare

Download or read book Fractional Statistics and Quantum Theory written by Avinash Khare and published by World Scientific. This book was released on 2005 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ChernOCoSimons theories. Topics covered here include ChernOCoSimons 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

Author : Alberto Lerda
Publisher : Springer Science & Business Media
ISBN 13 : 3540474668
Total Pages : 143 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Anyons by : Alberto Lerda

Download or read book Anyons written by Alberto Lerda and published by Springer Science & Business Media. This book was released on 2008-09-11 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Quantum Theory

Author : Avinash Khare
Publisher : World Scientific
ISBN 13 : 9812561609
Total Pages : 316 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Fractional Statistics and Quantum Theory by : Avinash Khare

Download or read book Fractional Statistics and Quantum Theory written by Avinash Khare and published by World Scientific. This book was released on 2005 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractional Dynamics

Author : Joseph Klafter
Publisher : World Scientific
ISBN 13 : 9814340588
Total Pages : 530 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Fractional Dynamics by : Joseph Klafter

Download or read book Fractional Dynamics written by Joseph Klafter and published by World Scientific. This book was released on 2012 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides the latest developments in the field of fractional dynamics, which covers fractional (anomalous) transport phenomena, fractional statistical mechanics, fractional quantum mechanics and fractional quantum field theory. The contributors are selected based on their active and important contributions to their respective topics. This volume is the first of its kind that covers such a comprehensive range of topics in fractional dynamics. It will point out to advanced undergraduate and graduate students, and young researchers the possible directions of research in this subject. In addition to those who intend to work in this field and those already in the field, this volume will also be useful for researchers not directly involved in the field, but want to know the current status and trends of development in this subject. This latter group includes theoretical chemists, mathematical biologists and engineers.

Economic Dynamics with Memory

Author : Vasily E. Tarasov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110624818
Total Pages : 562 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Economic Dynamics with Memory by : Vasily E. Tarasov

Download or read book Economic Dynamics with Memory written by Vasily E. Tarasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-01-18 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs which cover progresses in fractional calculus research in mathematics and applications in physics, mechanics, engineering and biology etc. Methodological aspects e.g., theory, modeling and computational methods are presented from mathematical point of view, and emphases are placed in computer simulation, analysis, design and control of application-oriented issues in various scientific disciplines. It is designed for mathematicians, and researchers using fractional calculus as a tool in the field of physics, mechanics, engineering and biology. Contributions which are interdisciplinary and which stimulate further research at the crossroads of sciences and engineering are particularly welcomed. Editor-in-chief: Changpin Li, Shanghai University, China Editorial Board: Virginia Kiryakova, Bulgarian Academy of Sciences, Bulgaria Francesco Mainardi, University of Bologna, Italy Dragan Spasic, University of Novi Sad, Serbia Bruce Ian Henry, University of New South Wales, Australia YangQuan Chen, University of California, Merced, USA Please submit book proposals to Leonardo Milla, [email protected]

Fractional Quantum Hall Effects: New Developments

Author : Bertrand I Halperin
Publisher : World Scientific
ISBN 13 : 9811217505
Total Pages : 551 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Fractional Quantum Hall Effects: New Developments by : Bertrand I Halperin

Download or read book Fractional Quantum Hall Effects: New Developments written by Bertrand I Halperin and published by World Scientific. This book was released on 2020-06-09 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fractional quantum Hall effect has been one of the most active areas of research in quantum condensed matter physics for nearly four decades, serving as a paradigm for unexpected and exotic emergent behavior arising from interactions. This book, featuring a collection of articles written by experts and a Foreword by Klaus von Klitzing, the discoverer of quantum Hall effect and winner of 1985 Nobel Prize in physics, aims to provide a coherent account of the exciting new developments and the current status of the field.

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

Author : Hagen Kleinert
Publisher : World Scientific
ISBN 13 : 9814273570
Total Pages : 1626 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets by : Hagen Kleinert

Download or read book Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets written by Hagen Kleinert and published by World Scientific. This book was released on 2009 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractional Calculus

Author : Richard Herrmann
Publisher : World Scientific
ISBN 13 : 9814340243
Total Pages : 274 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Fractional Calculus by : Richard Herrmann

Download or read book Fractional Calculus written by Richard Herrmann and published by World Scientific. This book was released on 2011 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus is undergoing rapidly and ongoing development. We can already recognize, that within its framework new concepts and strategies emerge, which lead to new challenging insights and surprising correlations between different branches of physics. This book is an invitation both to the interested student and the professional researcher. It presents a thorough introduction to the basics of fractional calculus and guides the reader directly to the current state-of-the-art physical interpretation. It is also devoted to the application of fractional calculus on physical problems, in the subjects of classical mechanics, friction, damping, oscillations, group theory, quantum mechanics, nuclear physics, and hadron spectroscopy up to quantum field theory.

Advanced Quantum Mechanics

Author : Guangjiong Ni
Publisher :
ISBN 13 : 9781589490109
Total Pages : 0 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Advanced Quantum Mechanics by : Guangjiong Ni

Download or read book Advanced Quantum Mechanics written by Guangjiong Ni and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fractional Derivatives for Physicists and Engineers

Author : Vladimir V. Uchaikin
Publisher : Springer Science & Business Media
ISBN 13 : 3642339115
Total Pages : 385 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Fractional Derivatives for Physicists and Engineers by : Vladimir V. Uchaikin

Download or read book Fractional Derivatives for Physicists and Engineers written by Vladimir V. Uchaikin and published by Springer Science & Business Media. This book was released on 2013-07-09 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. Fractional Derivatives for Physicists and Engineers— The first volume contains a clear introduction into such a modern branch of analysis as the fractional calculus. The second develops a wide panorama of applications of the fractional calculus to various physical problems. This book recovers new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular. Prof. Vladimir V. UCHAIKIN is a known Russian scientist and pedagogue, a Honored Worker of Russian High School, a member of the Russian Academy of Natural Sciences. He is the author of about three hundreds articles and more than a dozen books (mostly in Russian) in Cosmic ray physics, Mathematical physics, Levy stable statistics, Monte Carlo methods with applications to anomalous processes in complex systems of various levels: from quantum dots to the Milky Way galaxy.

Fractional Calculus

Author : Herrmann Richard
Publisher : World Scientific
ISBN 13 : 981327459X
Total Pages : 636 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Fractional Calculus by : Herrmann Richard

Download or read book Fractional Calculus written by Herrmann Richard and published by World Scientific. This book was released on 2001-02-12 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a concise introduction to the basic methods and strategies in fractional calculus which enables the reader to catch up with the state-of-the-art in this field and to participate and contribute in the development of this exciting research area. This book is devoted to the application of fractional calculus on physical problems. The fractional concept is applied to subjects in classical mechanics, image processing, folded potentials in cluster physics, infrared spectroscopy, group theory, quantum mechanics, nuclear physics, hadron spectroscopy up to quantum field theory and will surprise the reader with new intriguing insights. This new, extended edition includes additional chapters about numerical solution of the fractional Schrödinger equation, self-similarity and the geometric interpretation of non-isotropic fractional differential operators. Motivated by the positive response, new exercises with elaborated solutions are added, which significantly support a deeper understanding of the general aspects of the theory. Besides students as well as researchers in this field, this book will also be useful as a supporting medium for teachers teaching courses devoted to this subject.

Fractional Dynamics

Author : Vasily E. Tarasov
Publisher : Springer Science & Business Media
ISBN 13 : 3642140033
Total Pages : 504 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Fractional Dynamics by : Vasily E. Tarasov

Download or read book Fractional Dynamics written by Vasily E. Tarasov and published by Springer Science & Business Media. This book was released on 2011-01-04 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.

Emergent Quantum Mechanics

Author : Jan Walleczek
Publisher : MDPI
ISBN 13 : 3038976164
Total Pages : 544 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis Emergent Quantum Mechanics by : Jan Walleczek

Download or read book Emergent Quantum Mechanics written by Jan Walleczek and published by MDPI. This book was released on 2019-04-02 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in "deeper-level" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de Broglie-Bohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeper-level questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and non-classical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.

Advances in Fractional Calculus

Author : J. Sabatier
Publisher : Springer Science & Business Media
ISBN 13 : 1402060424
Total Pages : 550 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Advances in Fractional Calculus by : J. Sabatier

Download or read book Advances in Fractional Calculus written by J. Sabatier and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Quantum Mechanics of Non-Hamiltonian and Dissipative Systems

Author : Vasily Tarasov
Publisher : Elsevier
ISBN 13 : 9780080559711
Total Pages : 530 pages
Book Rating : 4.5/5 (597 download)

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Book Synopsis Quantum Mechanics of Non-Hamiltonian and Dissipative Systems by : Vasily Tarasov

Download or read book Quantum Mechanics of Non-Hamiltonian and Dissipative Systems written by Vasily Tarasov and published by Elsevier. This book was released on 2008-06-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006. • Requires no preliminary knowledge of graduate and advanced mathematics • Discusses the fundamental results of last 15 years in this theory • Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences

The Quantum Hall Effect

Author : Daijiro Yoshioka
Publisher : Springer Science & Business Media
ISBN 13 : 3662050161
Total Pages : 214 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis The Quantum Hall Effect by : Daijiro Yoshioka

Download or read book The Quantum Hall Effect written by Daijiro Yoshioka and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fractional quantum Hall effect has opened up a new paradigm in the study of strongly correlated electrons and it has been shown that new concepts, such as fractional statistics, anyon, chiral Luttinger liquid and composite particles, are realized in two-dimensional electron systems. This book explains the quantum Hall effects together with these new concepts starting from elementary quantum mechanics.