Topological Phase Transitions And New Developments
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Topological Phase Transitions And New Developments
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Author : Lars Brink
language : en
Publisher: World Scientific
Release Date : 2018-08-13
Topological Phase Transitions And New Developments written by Lars Brink and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-13 with Science categories.
Geometry and topology have been a fascination in physics since the start of the 20th century. A leading example is Einstein's geometrical theory of gravity. At the beginning of the 1970s, topological ideas entered areas of condensed matter physics. These advances were driven by new seminal ideas resolving a serious contradiction between experiment and the standard interpretation of a rigorous mathematical theorem which led to the study of new exotic topological phases of matter. Topological defect driven phase transitions in thin, two dimensional films of superfluids, superconductors and crystals have provided great insight into the mechanism governing these topological phases present in those physical systems. Moreover, many of these topological properties remain 'protected' against disorder and topological distortion perturbations. An example of possible applications of such robustness to perturbations is in the search for encoding information in quantum computers, potentially providing the platform for fault-tolerant quantum computations.In the past four decades, the discovery of topological phases engendered great interest in condensed matter physics. It also attracted the attention of researchers working on quantum information, quantum materials and simulations, high energy physics and string theory. This unique volume contains articles written by some of the most prominent names in the field, including Nobel Laureate John Michael Kosterlitz and Professor Jorge V José. They originate from talks and discussions by leading experts at a recent workshop. They review previous works as well as addressing contemporary developments in the most pressing and important issues on various aspects of topological phases and topological phase transitions.
Topological Phases Of Matter
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Author : Roderich Moessner
language : en
Publisher: Cambridge University Press
Release Date : 2021-04-29
Topological Phases Of Matter written by Roderich Moessner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-29 with Mathematics categories.
This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.
Fractional Quantum Hall Effects New Developments
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Author : Bertrand I Halperin
language : en
Publisher: World Scientific
Release Date : 2020-06-09
Fractional Quantum Hall Effects New Developments written by Bertrand I Halperin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-09 with Science categories.
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.
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.
Complex Nonlinearity
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Author : Vladimir G. Ivancevic
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-31
Complex Nonlinearity written by Vladimir G. Ivancevic 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 2008-05-31 with Science categories.
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
Equilibrium Statistical Physics
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Author : M. Baus
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-15
Equilibrium Statistical Physics written by M. Baus 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 2007-11-15 with Science categories.
This is a textbook which gradually introduces the student to the statistical mechanical study of the different phases of matter and to the phase transitions between them. Throughout, only simple models of both ordinary and soft matter are used but these are studied in full detail. The subject is developed in a pedagogical manner, starting from the basics, going from the simple ideal systems to the interacting systems, and ending with the more modern topics. The textbook provides the student with a complete overview, intentionally at an introductory level, of the theory of phase transitions. All equations and deductions are included.
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.
Density Functional Theory
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Author : Eberhard Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-14
Density Functional Theory written by Eberhard Engel 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 2011-02-14 with Science categories.
Density Functional Theory (DFT) has firmly established itself as the workhorse for atomic-level simulations of condensed phases, pure or composite materials and quantum chemical systems. This work offers a rigorous and detailed introduction to the foundations of this theory, up to and including such advanced topics as orbital-dependent functionals as well as both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, the text concentrates on the self-contained presentation of the basics of the most widely used DFT variants: this implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating the strengths and weaknesses of particular approaches or functionals. The structure and content of this book allow a tutorial and modular self-study approach: the reader will find that all concepts of many-body theory which are indispensable for the discussion of DFT - such as the single-particle Green's function or response functions - are introduced step by step, along with the actual DFT material. The same applies to basic notions of solid state theory, such as the Fermi surface of inhomogeneous, interacting systems. In fact, even the language of second quantization is introduced systematically in an Appendix for readers without formal training in many-body theory.
Topological Aspects Of Condensed Matter Physics
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Author : Claudio Chamon
language : en
Publisher: Oxford University Press
Release Date : 2017
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 with Science categories.
This book contains lecture notes by world experts on topological quantum phenomena, which are being developed at unprecedented rates in novel material systems.
Introduction To Topological Quantum Computation
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Author : Jiannis K. Pachos
language : en
Publisher: Cambridge University Press
Release Date : 2012-04-12
Introduction To Topological Quantum Computation written by Jiannis K. Pachos and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-12 with Computers categories.
Ideal for graduate students and researchers from various sub-disciplines, this book provides an excellent introduction to topological quantum computation.