Topological Phase Transitions And New Developments

Author : Jose Jorge V,Phua Kok Khoo,Brink Lars
Publisher : World Scientific
Page : 264 pages
File Size : 50,9 Mb
Release : 2018-08-10
Category : Science
ISBN : 9789813271357

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Topological Phase Transitions and New Developments by Jose Jorge V,Phua Kok Khoo,Brink Lars Pdf

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.

Author : Lokman Tsui
Publisher : Unknown
Page : 98 pages
File Size : 48,8 Mb
Release : 2018
Category : Electronic
ISBN : OCLC:1066229244

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Topological Phase Transitions by Lokman Tsui Pdf

The study of continuous phase transitions triggered by spontaneous symmetry breaking has brought revolutionary ideas to physics. Recently, through the discovery of symmetry protected topological phases, it is realized that continuous quantum phase transition can also occur between states with the same symmetry but different topology. The subject of this dissertation is the phase transition between these symmetry protected topological states (SPTs). There are two main parts in this dissertation. In the first part we consider spatial dimension $d$ and symmetry group $G$ so that the cohomology group, $H^{d+1}(G,U(1))$, contains at least one $Z_{2n}$ or $Z$ factor. We show that the phase transition between the trivial SPT and the root states that generate the $ Z_{2n} $ or $Z$ groups can be induced on the boundary of a d+1 dimensional $G\times Z_2^T$-symmetric SPT by a $Z_2^T$ symmetry breaking field. Moreover we show these boundary phase transitions can be ``transplanted'' to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase. In the second part, we study the phase transition between bosonic topological phases protected by $Z_n\times Z_n$ in 1+1 dimensions. We find a direct transition occurs when $ n=2,3,4 $ and in all cases the critical point possesses two gap opening relevant operators: one leads to a Landau-forbidden symmetry breaking phase transition and the other to the topological phase transition. We also obtained a constraint($ c\geq1 $) on the central charge for general phase transitions between symmetry protected bosonic topological phases in 1+1D.

Author : Pierre Papon,Jacques Leblond,Paul H.E. Meijer
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 45,7 Mb
Release : 2007-07-27
Category : Science
ISBN : 9783540333906

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The Physics of Phase Transitions by Pierre Papon,Jacques Leblond,Paul H.E. Meijer Pdf

This book occupies an important place at the crossroads of several fields central to materials sciences. The expanded second edition incorporates new developments in the states of matter physics, and includes end-of-chapter problems and complete answers.

Author : Roderich Moessner,Joel E. Moore
Publisher : Cambridge University Press
Page : 393 pages
File Size : 42,5 Mb
Release : 2021-04-29
Category : Mathematics
ISBN : 9781107105539

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Topological Phases of Matter by Roderich Moessner,Joel E. Moore Pdf

This important graduate level text unites the physical mechanisms behind the phenomena of topological matter within a theoretical framework.

Author : Bertrand I Halperin,Jainendra K Jain
Publisher : World Scientific
Page : 551 pages
File Size : 50,7 Mb
Release : 2020-06-09
Category : Science
ISBN : 9789811217500

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Fractional Quantum Hall Effects: New Developments by Bertrand I Halperin,Jainendra K Jain Pdf

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.

Author : Yuriy M. Bunkov,Henri Godfrin
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 51,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401141062

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Topological Defects and the Non-Equilibrium Dynamics of Symmetry Breaking Phase Transitions by Yuriy M. Bunkov,Henri Godfrin Pdf

Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.

Author : Anonim
Publisher : Elsevier
Page : 337 pages
File Size : 49,9 Mb
Release : 2000-09-15
Category : Science
ISBN : 9780080538754

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Phase Transitions and Critical Phenomena by Anonim Pdf

The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. No longer an area of specialist interest, it has acquired a central focus in condensed matter studies. The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.The two review articles in this volume complement each other in a remarkable way. Both deal with what might be called the modern geometricapproach to the properties of macroscopic systems. The first article by Georgii (et al.) describes how recent advances in the application ofgeometric ideas leads to a better understanding of pure phases and phase transitions in equilibrium systems. The second article by Alava (et al.)deals with geometrical aspects of multi-body systems in a hands-on way, going beyond abstract theory to obtain practical answers. Thecombination of computers and geometrical ideas described in this volume will doubtless play a major role in the development of statisticalmechanics in the twenty-first century.

Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 44,9 Mb
Release : 2006-02-04
Category : Science
ISBN : 9783540312642

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Topology in Condensed Matter by Michael I. Monastyrsky Pdf

This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.

Author : Tian Ma,Shouhong Wang
Publisher : Springer Nature
Page : 757 pages
File Size : 54,6 Mb
Release : 2019-11-08
Category : Mathematics
ISBN : 9783030292607

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Phase Transition Dynamics by Tian Ma,Shouhong Wang Pdf

This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields. This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity). Reviews of first edition: “The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. ... The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences.” (Carlo Bianca, Mathematical Reviews, December, 2014) “This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. ... The book is a very useful literature not only for the professionals in the field of dynamic systems and phase transitions but also for graduate students due to its interdisciplinary coverage and state-of-the-art level.” (Vladimir Čadež, zbMATH, Vol. 1285, 2014)

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 55,5 Mb
Release : 2013
Category : Electronic
ISBN : OCLC:944117350

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Topological Phase Transitions Driven by Non-Abelian Anyons by Anonim Pdf

Author : Minoru Fujimoto
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 41,8 Mb
Release : 2013-04-09
Category : Science
ISBN : 9781475727258

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The Physics of Structural Phase Transitions by Minoru Fujimoto Pdf

Intended for readers with some prior knowledge of condensed-matter physics, this text emphasises the basic physics behind spontaneous structural changes in crystals. Starting with the relevant thermodynamic principles, the author discusses the nature of order variables and their collective motion in a crystal lattice. He also goes on to describe experimental methods for modulated crystal structures and gives examples of structural changes in representative systems. Both a graduate text and reference work.

Author : Subir Sachdev
Publisher : Cambridge University Press
Page : 374 pages
File Size : 43,5 Mb
Release : 2001-04-23
Category : Mathematics
ISBN : 0521004543

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Quantum Phase Transitions by Subir Sachdev Pdf

Quantum Phase Transitions is the first book to describe in detail the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The subject plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials. The author begins by developing the theory of quantum phase transitions in the simplest possible class of non-disordered, interacting systems - the quantum Ising and rotor models. Particular attention is paid to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Several other quantum phase transitions of increasing complexity are then discussed and clarified. Throughout, the author interweaves experimental results with presentation of theoretical models, and well over 500 references are included. The book will be of great interest to graduate students and researchers in condensed matter physics.

Author : Lincoln Carr
Publisher : CRC Press
Page : 756 pages
File Size : 42,6 Mb
Release : 2010-11-02
Category : Science
ISBN : 9781439802618

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Understanding Quantum Phase Transitions by Lincoln Carr Pdf

Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivit

Author : Anne-Christine Davis,Robert Brandenberger
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461518839

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Formation and Interactions of Topological Defects by Anne-Christine Davis,Robert Brandenberger Pdf

Topological defects have recently become of great interest in condensed matter physics, particle physics and cosmology. They are the unavoidable remnants of many symmetry breaking phase transitions. Topological defects can play an important role in describing the properties of many condensed matter systems (e.g. superfluids and superconduc tors); they can catalyze many unusual effects in particle physics models and they may be responsible for seeding the density perturbations in the early Universe which de velop into galaxies and the large-scale structure of the Universe. Topological defects are also of great interest in mathematics as nontrivial solutions of nonlinear differential equations stabilized by topological effects. The purpose of the Advanced Study Institute "Formation and Interactions of Topo logical Defects" was to bring together students and practitioners in condensed matter physics, particle physics and cosmology, to give a detailed exposition of the role of topo logical defects in these fields; to explore similarities and differences in the approaches; and to provide a common basis for discussion and future collaborative research on common problems.

Author : Uskali Mäki,Ioannis Votsis,Stéphanie Ruphy,Gerhard Schurz
Publisher : Springer
Page : 391 pages
File Size : 40,5 Mb
Release : 2015-09-09
Category : Science
ISBN : 9783319230153

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Recent Developments in the Philosophy of Science: EPSA13 Helsinki by Uskali Mäki,Ioannis Votsis,Stéphanie Ruphy,Gerhard Schurz Pdf

This volume showcases the best of recent research in the philosophy of science. A compilation of papers presented at the EPSA 13, it explores a broad distribution of topics such as causation, truthlikeness, scientific representation, gender-specific medicine, laws of nature, science funding and the wisdom of crowds. Papers are organised into headings which form the structure of the book. Readers will find that it covers several major fields within the philosophy of science, from general philosophy of science to the more specific philosophy of physics, philosophy of chemistry, philosophy of the life sciences, philosophy of psychology, and philosophy of the social sciences and humanities, amongst others. This volume provides an excellent overview of the state of the art in the philosophy of science, as practiced in different European countries and beyond. ​It will appeal to researchers with an interest in the philosophical underpinnings of their own discipline, and to philosophers who wish to explore the latest work on the themes explored.