Anyons
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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.
Physics And Mathematics Of Anyons Proceedings Of The Tcsuh Workshop
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Author : C S Ting
language : en
Publisher: World Scientific
Release Date : 1991-06-14
Physics And Mathematics Of Anyons Proceedings Of The Tcsuh Workshop written by C S Ting and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-14 with categories.
In this volume, the fractional quantum Hall effect is reviewed and reexamined with emphasis on the fractional statistics. Possible relevance of the anyon idea to high temperature superconductivity is addressed both theoretically and experimentally.
Topologically Ordered Zigzag Nanoribbon E 2 Fractionally Charged Anyons And Spin Charge Separation
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Author : Eric Sung Ryul Yang
language : en
Publisher: World Scientific
Release Date : 2023-03-21
Topologically Ordered Zigzag Nanoribbon E 2 Fractionally Charged Anyons And Spin Charge Separation written by Eric Sung Ryul Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-21 with Science categories.
This is the first graduate level textbook of topologically ordered phases with emphasis on graphene zigzag nanoribbons. It also explains common properties of several other topologically ordered phases as well as the e/2 fractional charge quantization and spin-charge separation of an electron.
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
The Diverse World Of Pdes
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Author : I. S. Krasil′shchik
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-23
The Diverse World Of Pdes written by I. S. Krasil′shchik and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-23 with Mathematics categories.
This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.
Topological Quantum Computation
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Author : Zhenghan Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Topological Quantum Computation written by Zhenghan Wang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Computers categories.
Topological quantum computation is a computational paradigm based on topological phases of matter, which are governed by topological quantum field theories. In this approach, information is stored in the lowest energy states of many-anyon systems and processed by braiding non-abelian anyons. The computational answer is accessed by bringing anyons together and observing the result. Besides its theoretical esthetic appeal, the practical merit of the topological approach lies in its error-minimizing hypothetical hardware: topological phases of matter are fault-avoiding or deaf to most local noises, and unitary gates are implemented with exponential accuracy. Experimental realizations are pursued in systems such as fractional quantum Hall liquids and topological insulators. This book expands on the author's CBMS lectures on knots and topological quantum computing and is intended as a primer for mathematically inclined graduate students. With an emphasis on introducing basic notions and current research, this book gives the first coherent account of the field, covering a wide range of topics: Temperley-Lieb-Jones theory, the quantum circuit model, ribbon fusion category theory, topological quantum field theory, anyon theory, additive approximation of the Jones polynomial, anyonic quantum computing models, and mathematical models of topological phases of matter.
Topological Orders With Spins And Fermions
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Author : Laura Ortiz Martín
language : en
Publisher: Springer
Release Date : 2019-07-11
Topological Orders With Spins And Fermions written by Laura Ortiz Martín and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-11 with Science categories.
This thesis deals with topological orders from two different perspectives: from a condensed matter point of view, where topological orders are considered as breakthrough phases of matter; and from the emerging realm of quantum computation, where topological quantum codes are considered the most appealing platform against decoherence. The thesis reports remarkable studies from both sides. It thoroughly investigates a topological order called the double semion model, a counterpart of the Kitaev model but exhibiting richer quasiparticles as excitations. A new model for symmetry enriched topological order is constructed, which adds an onsite global symmetry to the double semion model. Using this topological phase, a new example of topological code is developed, the semion code, which is non-CSS, additive, non-Pauli and within the stabiliser formalism. Furthermore, the thesis analyses the Rashba spin-orbit coupling within topological insulators, turning the helical edge states into generic edges modes with potential application in spinstronics. New types of topological superconductors are proposed and the novel properties of the correspondingly created Majorana fermions are investigated. These Majorana fermions have inherent properties enabling braiding and the performance of logical gates as fundamental blocks for a universsal quantum computator.
Topology And Condensed Matter Physics
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Author : Somendra Mohan Bhattacharjee
language : en
Publisher: Springer
Release Date : 2017-12-20
Topology And Condensed Matter Physics written by Somendra Mohan Bhattacharjee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-20 with Science categories.
This book introduces aspects of topology and applications to problems in condensed matter physics. Basic topics in mathematics have been introduced in a form accessible to physicists, and the use of topology in quantum, statistical and solid state physics has been developed with an emphasis on pedagogy. The aim is to bridge the language barrier between physics and mathematics, as well as the different specializations in physics. Pitched at the level of a graduate student of physics, this book does not assume any additional knowledge of mathematics or physics. It is therefore suited for advanced postgraduate students as well. A collection of selected problems will help the reader learn the topics on one's own, and the broad range of topics covered will make the text a valuable resource for practising researchers in the field. The book consists of two parts: one corresponds to developing the necessary mathematics and the other discusses applications to physical problems. The section on mathematics is a quick, but more-or-less complete, review of topology. The focus is on explaining fundamental concepts rather than dwelling on details of proofs while retaining the mathematical flavour. There is an overview chapter at the beginning and a recapitulation chapter on group theory. The physics section starts with an introduction and then goes on to topics in quantum mechanics, statistical mechanics of polymers, knots, and vertex models, solid state physics, exotic excitations such as Dirac quasiparticles, Majorana modes, Abelian and non-Abelian anyons. Quantum spin liquids and quantum information-processing are also covered in some detail.
Symmetries And Groups In Contemporary Physics
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Author : Chengming Bai
language : en
Publisher: World Scientific
Release Date : 2013-07-26
Symmetries And Groups In Contemporary Physics written by Chengming Bai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-26 with Mathematics categories.
This volume focuses on developments in the field of group theory in its broadest sense and is of interest to theoretical and experimental physicists, mathematicians, and scientists in related disciplines who are interested in the latest methods and applications. In an increasingly ultra-specialized world, this volume will demonstrate the interchange of ideas and methods in theoretical and mathematical physics. Contents:The Wigner MedalThe Hermann Weyl PrizePlenary SessionParallel Sessions:Nonlinear SciencesQuantum AlgebrasSuperintegrable HamiltoniansApplications in BiologyQuantum Information and Representation TheoryFinite Quantum Systems and Combinatorial PhysicsSymmetries in String Theory and SupergravityLoop Quantum GravityTensor and Group Field Theories for Quantum GravityConformal Field TheoriesSupersymmetry and Quantum GroupsApplications in Particle and Nuclear PhysicsGeneral Quantum Mechanics and Its Mathematical Methods Involving Group TheoryPoster Session Readership: Researchers and specialists in group theory and its applications to mathematics, physics and other fields in natural science. Keywords:Symmetries;Group Theory;Quantum Physics;Coherent States;Quantum Information;Nonlinear Physics;Supersymmetry;Quantum Gravity;Strings;Conformal Fields;Tensor Fields;Mathematical Biology;Particle Physics;Quantum Algebras;Foundations Of Quantum Mechanics;Combinatorial PhysicsKey Features:Wide range of topics in theoretical and mathematical physicsContains the most recent developments in innovative fields like quantum information, physics and biology, quantum gravity (e.g., strings, loop, tensor fields approaches), combinatorial physicsCross-sectional view of these developments given by prominent specialists, be they promising young scientists (e.g. Gurau, Chiribella, etc.) or confirmed researchers (e.g., Lewandowski, Batchelor, Wang, Murakami, Busch, etc.)
Quantum Computation
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Author : Samuel J. Lomonaco
language : en
Publisher: American Mathematical Soc.
Release Date :
Quantum Computation written by Samuel J. Lomonaco and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Education categories.
This book presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, D.C. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field. Interrelationships with existing mathematical research areas were emphasized as much as possible. Moreover, the course was designed so that participants with little background in quantum mechanics would, upon completion, be prepared to begin reading the research literature on quantum computation and quantum information science. Based on audience feedback and questions, the written versions of the lectures have been greatly expanded, and supplementary material has been added. The book features an overview of relevant parts of quantum mechanics with an introduction to quantum computation, including many potential quantum mechanical computing devices; introduction to quantum algorithms and quantum complexity theory; in-depth discussion on quantum error correcting codes and quantum cryptography; and finally, exploration into diverse connections between quantum computation and various areas of mathematics and physics. This book is the companion volume to Quantum Computation and Quantum Information, CONM/305, Volume 305 in the Contemporary Mathematics series.