Topological Quantum Numbers In Nonrelativistic Physics
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Author | : D. J. Thouless |
Publisher | : World Scientific |
Total Pages | : 440 |
Release | : 1998 |
Genre | : Science |
ISBN | : 9810229003 |
Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect, solids and liquid crystals, and topological phase transitions. The accompanying reprints include some of the classic experimental and theoretical papers in this area.Physicists ? both experimental and theoretical ? who are interested in the topic will find this book an invaluable reference.
Author | : David Thouless |
Publisher | : World Scientific |
Total Pages | : 440 |
Release | : 1998-03-12 |
Genre | : Science |
ISBN | : 9814498033 |
Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect, solids and liquid crystals, and topological phase transitions. The accompanying reprints include some of the classic experimental and theoretical papers in this area.Physicists — both experimental and theoretical — who are interested in the topic will find this book an invaluable reference.
Author | : Yongmin Cho |
Publisher | : World Scientific |
Total Pages | : 1156 |
Release | : 1998-04-04 |
Genre | : |
ISBN | : 9814545538 |
This volume is a collection of lectures on the current topics in various areas of physics which were presented at the Inauguration Conference of Asia-Pacific Center for Theoretical Physics.
Author | : Kai S Lam |
Publisher | : World Scientific Publishing Company |
Total Pages | : 458 |
Release | : 2009-08-24 |
Genre | : Science |
ISBN | : 9813107480 |
This textbook is mainly for physics students at the advanced undergraduate and beginning graduate levels, especially those with a theoretical inclination. Its chief purpose is to give a systematic introduction to the main ingredients of the fundamentals of quantum theory, with special emphasis on those aspects of group theory (spacetime and permutational symmetries and group representations) and differential geometry (geometrical phases, topological quantum numbers, and Chern-Simons Theory) that are relevant in modern developments of the subject. It will provide students with an overview of key elements of the theory, as well as a solid preparation in calculational techniques.
Author | : Álvaro Díaz Fernández |
Publisher | : Springer Nature |
Total Pages | : 183 |
Release | : 2020-12-09 |
Genre | : Science |
ISBN | : 3030615553 |
Dirac cones are ubiquitous to non-trivial quantum matter and are expected to boost and reshape the field of modern electronics. Particularly relevant examples where these cones arise are topological insulators and graphene. From a fundamental perspective, this thesis proposes schemes towards modifying basic properties of these cones in the aforementioned materials. The thesis begins with a brief historical introduction which is followed by an extensive chapter that endows the reader with the basic tools of symmetry and topology needed to understand the remaining text. The subsequent four chapters are devoted to the reshaping of Dirac cones by external fields and delta doping. At all times, the ideas discussed in the second chapter are always a guiding principle to understand the phenomena discussed in those four chapters. As a result, the thesis is cohesive and represents a major advance in our understanding of the physics of Dirac materials.
Author | : Jiannis K. Pachos |
Publisher | : Cambridge University Press |
Total Pages | : 220 |
Release | : 2012-04-12 |
Genre | : Science |
ISBN | : 1139936689 |
Combining physics, mathematics and computer science, topological quantum computation is a rapidly expanding research area focused on the exploration of quantum evolutions that are immune to errors. In this book, the author presents a variety of different topics developed together for the first time, forming an excellent introduction to topological quantum computation. The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way. Relevant calculations are fully explained, and numerous worked examples and exercises support and aid understanding. Special emphasis is given to the motivation and physical intuition behind every mathematical concept. Demystifying difficult topics by using accessible language, this book has broad appeal and is ideal for graduate students and researchers from various disciplines who want to get into this new and exciting research field.
Author | : Mike Guidry |
Publisher | : Cambridge University Press |
Total Pages | : 665 |
Release | : 2022-03-31 |
Genre | : Mathematics |
ISBN | : 1316518612 |
A pedagogical introduction to the modern applications of groups, algebras, and topology for undergraduate and graduate students in physics.
Author | : Eike Bick |
Publisher | : Springer Science & Business Media |
Total Pages | : 380 |
Release | : 2005-01-18 |
Genre | : Mathematics |
ISBN | : 9783540231257 |
Application of the concepts and methods of topology and geometry have led to a deeper understanding of many crucial aspects in condensed matter physics, cosmology, gravity and particle physics. This book can be considered an advanced textbook on modern applications and recent developments in these fields of physical research. Written as a set of largely self-contained extensive lectures, the book gives an introduction to topological concepts in gauge theories, BRST quantization, chiral anomalies, supersymmetric solitons and noncommutative geometry. It will be of benefit to postgraduate students, educating newcomers to the field and lecturers looking for advanced material.
Author | : Richard M. Martin |
Publisher | : Cambridge University Press |
Total Pages | : 791 |
Release | : 2020-08-27 |
Genre | : Mathematics |
ISBN | : 1108429904 |
An authoritative text in condensed matter physics, unifying theory and methods to present electronic structure to students and researchers.
Author | : Somendra Mohan Bhattacharjee |
Publisher | : Springer |
Total Pages | : 519 |
Release | : 2017-12-20 |
Genre | : Science |
ISBN | : 9811068410 |
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.