Topologically Protected States In One Dimensional Systems
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Topologically Protected States In One Dimensional Systems
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Author : Charles Fefferman
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-25
Topologically Protected States In One Dimensional Systems written by Charles Fefferman 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 2017-04-25 with Mathematics categories.
The authors study a class of periodic Schrodinger operators, which in distinguished cases can be proved to have linear band-crossings or ``Dirac points''. They then show that the introduction of an ``edge'', via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized ``edge states''. These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
Topologically Protected States In One Dimensional Systems
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Author : Charles Fefferman
language : en
Publisher:
Release Date : 2017
Topologically Protected States In One Dimensional Systems written by Charles Fefferman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Dirac equation categories.
We study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "mDirac points". We then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized "edge states". These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. Our model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states we construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
A Short Course On Topological Insulators
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Author : János K. Asbóth
language : en
Publisher: Springer
Release Date : 2016-02-22
A Short Course On Topological Insulators written by János K. Asbóth and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-22 with Science categories.
This course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.
Dynamics Of Partial Differential Equations
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Author : C. Eugene Wayne
language : en
Publisher: Springer
Release Date : 2015-08-08
Dynamics Of Partial Differential Equations written by C. Eugene Wayne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-08 with Mathematics categories.
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
Topology In Condensed Matter
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Author : Michael I. Monastyrsky
language : en
Publisher: Springer
Release Date : 2010-02-12
Topology In Condensed Matter written by Michael I. Monastyrsky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-12 with Science categories.
This volume is based on the talks and lectures given by the participants of the 3-month seminar program “Topology in Condensed Matter,” which was held in the MPIPKS Dresden, 8 May–31 July 2002 under the scienti?c direction of Professors M. Kleman, S. Novikov, and myself. The aim of this program was to discuss recent applications of topology to several areas in condensed matter physics and related ?elds like biology. The last 30 years of the development of modern physics a?rmed two important ideas. The ?rst is the e?cient applications of topology in physics. One should mention applications in condensed matter, such as classi?cation of defects and textures in liquid crystals and super?uid liquids, the role of entangibility in polymer physics and DNA structures. The second tendency is also very prevalent. Some important discoveries in particle physics and condensed m- ter led to new and unpredictable questions in pure mathematics. We refer to the invention of monopoles and instantons in quantum ?eld theory, q- sicrystals ?uid membranes of high genus, fullerenes (C ,C , etc. ), and so on 60 90 in condensed matter. The number of such applications in the last years has increased substantially. The papers presented in this volume and the next one “Topology in - ology” re?ect the spectrum of topics discussed. Besides original papers, a mini-course in topology for physicists and biologists was organized. These lectures will be published in the second volume.
Topological Insulators
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Author : Shun-Qing Shen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-11
Topological Insulators written by Shun-Qing Shen 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 2013-01-11 with Technology & Engineering categories.
Topological insulators are insulating in the bulk, but process metallic states present around its boundary owing to the topological origin of the band structure. The metallic edge or surface states are immune to weak disorder or impurities, and robust against the deformation of the system geometry. This book, the first of its kind on topological insulators, presents a unified description of topological insulators from one to three dimensions based on the modified Dirac equation. A series of solutions of the bound states near the boundary are derived, and the existing conditions of these solutions are described. Topological invariants and their applications to a variety of systems from one-dimensional polyacetalene, to two-dimensional quantum spin Hall effect and p-wave superconductors, and three-dimensional topological insulators and superconductors or superfluids are introduced, helping readers to better understand this fascinating new field. This book is intended for researchers and graduate students working in the field of topological insulators and related areas. Shun-Qing Shen is a Professor at the Department of Physics, the University of Hong Kong, China.
Topological States For New Modes Of Information Storage And Transfer
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Author : Prabhakar Bandaru
language : en
Publisher: Springer Nature
Release Date : 2022-02-24
Topological States For New Modes Of Information Storage And Transfer written by Prabhakar Bandaru and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-24 with Technology & Engineering categories.
This book reviews evidence for the existence of information storing states present in specific materials systems called Topological Materials. It discusses how quantum computation, a possible technology for the future, demands unique paradigms where the information storing states are just not disturbed by classical forces. They are protected from environmental disturbance, suggesting that whatever information is stored in such states would could be safe forever. The authors explain how the topological aspect arises from the configuration or the shape of energy space. He further explains that the existence of related topological states has not been conclusively established in spite of significant experimental effort over the past decade. And The book as such illustrates the necessity for such investigations as well as application of the topological states for new computational technologies. The scope of coverage includes all the necessary mathematical and physics preliminaries (starting at the undergraduate level) enabling researchers to quickly understand the state of the art literature.
Topological Insulators
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Author : Gregory Tkachov
language : en
Publisher: CRC Press
Release Date : 2015-10-14
Topological Insulators written by Gregory Tkachov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-14 with Science categories.
This book is the result of dynamic developments that have occurred in condensed matter physics after the recent discovery of a new class of electronic materials: topological insulators. A topological insulator is a material that behaves as a band insulator in its interior, while acting as a metallic conductor at its surface. The surface current car
Hypercontractivity In Group Von Neumann Algebras
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Author : Marius Junge
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-25
Hypercontractivity In Group Von Neumann Algebras written by Marius Junge 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 2017-09-25 with Mathematics categories.
In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive inequalities with respect to the Markov process given by the word length and with an even integer. Interpolation and differentiation also yield general hypercontrativity for via logarithmic Sobolev inequalities. The authors' method admits further applications to other discrete groups without small loops as far as the numerical part—which varies from one group to another—is implemented and tested on a computer. The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) hypercontractive inequalities for a larger class of groups/lengths, including any finitely generated group equipped with a conditionally negative word length, like infinite Coxeter groups. The authors' second method also yields hypercontractivity bounds for groups admitting a finite dimensional proper cocycle. Hypercontractivity fails for conditionally negative lengths in groups satisfying Kazhdan's property (T).
Topological Aspects Of Condensed Matter Physics
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Author : Claudio Chamon
language : en
Publisher: Oxford University Press
Release Date : 2017-02-16
Topological Aspects Of Condensed Matter Physics written by Claudio Chamon and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-16 with Science categories.
This book contains lecture notes by world experts on one of the most rapidly growing fields of research in physics. Topological quantum phenomena are being uncovered at unprecedented rates in novel material systems. The consequences are far reaching, from the possibility of carrying currents and performing computations without dissipation of energy, to the possibility of realizing platforms for topological quantum computation.The pedagogical lectures contained in this book are an excellent introduction to this blooming field. The lecture notes are intended for graduate students or advanced undergraduate students in physics and mathematics who want to immerse in this exciting XXI century physics topic. This Les Houches Summer School presents an overview of this field, along with a sense of its origins and its placement on the map of fundamental physics advancements. The School comprised a set of basic lectures (part 1) aimed at a pedagogical introduction of the fundamental concepts, which was accompanied by more advanced lectures (part 2) covering individual topics at the forefront of today's research in condensed-matter physics.