Geometric Phases In Physics

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Geometric Phases in Physics

Author : F Wilczek
Publisher : World Scientific
ISBN 13 : 981450758X
Total Pages : 528 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Geometric Phases in Physics by : F Wilczek

Download or read book Geometric Phases in Physics written by F Wilczek and published by World Scientific. This book was released on 1989-07-01 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ‘Berry's phase’) in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject. Contents:Introduction and OverviewAnticipationsFoundationsSome Applications and TestsFractional StatisticsQuantized Hall EffectWess-Zumino Terms and AnomaliesClassical SystemsAsymptotics Readership: Mathematical, high energy and condensed matter physicists.

Geometric Phases in Classical and Quantum Mechanics

Author : Dariusz Chruscinski
Publisher : Springer Science & Business Media
ISBN 13 : 0817681760
Total Pages : 337 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Geometric Phases in Classical and Quantum Mechanics by : Dariusz Chruscinski

Download or read book Geometric Phases in Classical and Quantum Mechanics written by Dariusz Chruscinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.

The Geometric Phase in Quantum Systems

Author : Arno Bohm
Publisher : Springer Science & Business Media
ISBN 13 : 3662103338
Total Pages : 447 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis The Geometric Phase in Quantum Systems by : Arno Bohm

Download or read book The Geometric Phase in Quantum Systems written by Arno Bohm and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "...useful for experts in mathematical physics...this is a very interesting book, which deserves to be found in any physical library." (OPTICS & PHOTONICS NEWS, July/August 2005).

Geometric Phases in Physics

Author : Frank Wilczek
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789971505998
Total Pages : 509 pages
Book Rating : 4.5/5 (59 download)

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Book Synopsis Geometric Phases in Physics by : Frank Wilczek

Download or read book Geometric Phases in Physics written by Frank Wilczek and published by World Scientific Publishing Company Incorporated. This book was released on 1989 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ch. 1. Introduction and overview -- ch. 2. Anticipations -- ch. 3. Foundations -- ch. 4. Some applications and tests -- ch. 5. Fractional statistics -- ch. 6. The quantized hall effect -- ch. 7. Wess-zumino terms and anomalies -- ch. 8. Classical systems -- ch. 9. Asymptotics

Physical Effects of Geometric Phases

Author : Qian Niu
Publisher : World Scientific
ISBN 13 : 9813225726
Total Pages : 424 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Physical Effects of Geometric Phases by : Qian Niu

Download or read book Physical Effects of Geometric Phases written by Qian Niu and published by World Scientific. This book was released on 2017-08-28 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berry phase has been widely used in condensed matter physics in the past two decades. This volume is a timely collection of essential papers in this important field, which is highlighted by 2016 Nobel Prize in physics and recent exciting developments in topological matters. Each chapter has an introduction, which helps readers to understand the reprints that follow.

Berry Phases in Electronic Structure Theory

Author : David Vanderbilt
Publisher : Cambridge University Press
ISBN 13 : 1108661300
Total Pages : 395 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Berry Phases in Electronic Structure Theory by : David Vanderbilt

Download or read book Berry Phases in Electronic Structure Theory written by David Vanderbilt and published by Cambridge University Press. This book was released on 2018-11-01 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past twenty-five years, mathematical concepts associated with geometric phases have come to occupy a central place in our modern understanding of the physics of electrons in solids. These 'Berry phases' describe the global phase acquired by a quantum state as the Hamiltonian is changed. Beginning at an elementary level, this book provides a pedagogical introduction to the important role of Berry phases and curvatures, and outlines their great influence upon many key properties of electrons in solids, including electric polarization, anomalous Hall conductivity, and the nature of the topological insulating state. It focuses on drawing connections between physical concepts and provides a solid framework for their integration, enabling researchers and students to explore and develop links to related fields. Computational examples and exercises throughout provide an added dimension to the book, giving readers the opportunity to explore the central concepts in a practical and engaging way.

Topology and Geometry for Physics

Author : Helmut Eschrig
Publisher : Springer
ISBN 13 : 3642147003
Total Pages : 397 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Topology and Geometry for Physics by : Helmut Eschrig

Download or read book Topology and Geometry for Physics written by Helmut Eschrig and published by Springer. This book was released on 2011-01-26 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.

Geometric Phases in Physics

Author : Frank Wilczek
Publisher : World Scientific
ISBN 13 : 9789971506216
Total Pages : 530 pages
Book Rating : 4.5/5 (62 download)

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Book Synopsis Geometric Phases in Physics by : Frank Wilczek

Download or read book Geometric Phases in Physics written by Frank Wilczek and published by World Scientific. This book was released on 1989 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ?Berry's phase?) in addition to the usual dynamical phase derived from Schrdinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject.

Lectures on Mechanics

Author : Jerrold E. Marsden
Publisher : Cambridge University Press
ISBN 13 : 9780521428446
Total Pages : 272 pages
Book Rating : 4.4/5 (284 download)

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Book Synopsis Lectures on Mechanics by : Jerrold E. Marsden

Download or read book Lectures on Mechanics written by Jerrold E. Marsden and published by Cambridge University Press. This book was released on 1992-04-30 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the 1991 LMS Invited Lectures given by Professor Marsden, this book discusses and applies symmetry methods to such areas as bifurcations and chaos in mechanical systems.

Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases

Author : Zhong-Can Ou-Yang
Publisher : World Scientific
ISBN 13 : 9789810232481
Total Pages : 252 pages
Book Rating : 4.2/5 (324 download)

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Book Synopsis Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases by : Zhong-Can Ou-Yang

Download or read book Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases written by Zhong-Can Ou-Yang and published by World Scientific. This book was released on 1999 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a comprehensive description of the mechanical equilibrium and deformation of membranes as a surface problem in differential geometry. Following the pioneering work by W Helfrich, the fluid membrane is seen as a nematic or smectic ? A liquid crystal film and its elastic energy form is deduced exactly from the curvature elastic theory of the liquid crystals. With surface variation the minimization of the energy at fixed osmotical pressure and surface tension gives a completely new surface equation in geometry that involves potential interest in mathematics. The investigations of the rigorous solution of the equation that have been carried out in recent years by the authors and their co-workers are presented here, among which the torus and the discocyte (the normal shape of the human red blood cell) may attract attention in cell biology. Within the framework of our mathematical model by analogy with cholesteric liquid crystals, an extensive investigation is made of the formation of the helical structures in a tilted chiral lipid bilayer, which has now become a hot topic in the fields of soft matter and biomembranes.

Analysis And Mathematical Physics

Author : Bullett Shaun
Publisher : World Scientific
ISBN 13 : 1786341018
Total Pages : 248 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Analysis And Mathematical Physics by : Bullett Shaun

Download or read book Analysis And Mathematical Physics written by Bullett Shaun and published by World Scientific. This book was released on 2016-12-22 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise reference book on analysis and mathematical physics, leading readers from a foundation to advanced level understanding of the topic. This is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as distributions, Fourier transforms and microlocal analysis, C* Algebras, value distribution of meromorphic functions, noncommutative differential geometry, differential geometry and mathematical physics, mathematical problems of general relativity, and special functions of mathematical physics. Analysis and Mathematical Physics is the sixth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

The Butterfly in the Quantum World

Author : Indubala I Satija
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681741172
Total Pages : 350 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis The Butterfly in the Quantum World by : Indubala I Satija

Download or read book The Butterfly in the Quantum World written by Indubala I Satija and published by Morgan & Claypool Publishers. This book was released on 2016-09-06 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.

Geometric Phases in Classical and Quantum Mechanics

Author : D. Chrus'cin'ski
Publisher :
ISBN 13 : 9783764342821
Total Pages : pages
Book Rating : 4.3/5 (428 download)

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Book Synopsis Geometric Phases in Classical and Quantum Mechanics by : D. Chrus'cin'ski

Download or read book Geometric Phases in Classical and Quantum Mechanics written by D. Chrus'cin'ski and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Defects and Geometry in Condensed Matter Physics

Author : David R. Nelson
Publisher : Cambridge University Press
ISBN 13 : 9780521004008
Total Pages : 396 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Defects and Geometry in Condensed Matter Physics by : David R. Nelson

Download or read book Defects and Geometry in Condensed Matter Physics written by David R. Nelson and published by Cambridge University Press. This book was released on 2002-03-18 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Mathematics for Physics

Author : Michael Stone
Publisher : Cambridge University Press
ISBN 13 : 1139480618
Total Pages : 821 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Mathematics for Physics by : Michael Stone

Download or read book Mathematics for Physics written by Michael Stone and published by Cambridge University Press. This book was released on 2009-07-09 with total page 821 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Quantum Scaling in Many-Body Systems

Author : Mucio Continentino
Publisher : Cambridge University Press
ISBN 13 : 1107150256
Total Pages : 249 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Quantum Scaling in Many-Body Systems by : Mucio Continentino

Download or read book Quantum Scaling in Many-Body Systems written by Mucio Continentino and published by Cambridge University Press. This book was released on 2017-04-17 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on experimental results, this updated edition approaches the problem of quantum phase transitions from a new and unifying perspective.

Topological Insulators and Topological Superconductors

Author : B. Andrei Bernevig
Publisher : Princeton University Press
ISBN 13 : 1400846730
Total Pages : 264 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Topological Insulators and Topological Superconductors by : B. Andrei Bernevig

Download or read book Topological Insulators and Topological Superconductors written by B. Andrei Bernevig and published by Princeton University Press. This book was released on 2013-04-07 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topological indices. The book also analyzes recent topics in condensed matter theory and concludes by surveying active subfields of research such as insulators with point-group symmetries and the stability of topological semimetals. Problems at the end of each chapter offer opportunities to test knowledge and engage with frontier research issues. Topological Insulators and Topological Superconductors will provide graduate students and researchers with the physical understanding and mathematical tools needed to embark on research in this rapidly evolving field.