Geometric Phases In Physics PDF Download
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Author: Alfred Shapere
Publisher: World Scientific
ISBN: 981450758X
Category : Mathematics
Languages : en
Pages : 527
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Book Description
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.
Author: Alfred Shapere
Publisher: World Scientific
ISBN: 981450758X
Category : Mathematics
Languages : en
Pages : 527
Get Book Here
Book Description
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.
Author: Dariusz Chruscinski
Publisher: Springer Science & Business Media
ISBN: 0817681760
Category : Mathematics
Languages : en
Pages : 346
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Book Description
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.
Author: Frank Wilczek
Publisher: World Scientific
ISBN: 9789971506216
Category : Science
Languages : en
Pages : 530
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Book Description
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.
Author: Arno Bohm
Publisher: Springer Science & Business Media
ISBN: 3662103338
Category : Science
Languages : en
Pages : 447
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Book Description
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).
Author: David Vanderbilt
Publisher: Cambridge University Press
ISBN: 1108661300
Category : Science
Languages : en
Pages : 395
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Book Description
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.
Author: Helmut Eschrig
Publisher: Springer
ISBN: 3642147003
Category : Science
Languages : en
Pages : 397
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Book Description
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.
Author: Daniel Greenberger
Publisher: Springer Science & Business Media
ISBN: 3540706267
Category : Science
Languages : en
Pages : 901
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Book Description
With contributions by leading quantum physicists, philosophers and historians, this comprehensive A-to-Z of quantum physics provides a lucid understanding of key concepts of quantum theory and experiment. It covers technical and interpretational aspects alike, and includes both traditional and new concepts, making it an indispensable resource for concise, up-to-date information about the many facets of quantum physics.
Author: Roberto Torretti
Publisher: Courier Corporation
ISBN: 0486690466
Category : Science
Languages : en
Pages : 417
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Book Description
Early in this century, it was shown that the new non-Newtonian physics -- known as Einstein's Special Theory of Relativity -- rested on a new, non-Euclidean geometry, which incorporated time and space into a unified "chronogeometric" structure. This high-level study elucidates the motivation and significance of the changes in physical geometry brought about by Einstein, in both the first and the second phase of Relativity. After a discussion of Newtonian principles and 19th-century views on electrodynamics and the aether, the author offers illuminating expositions of Einstein's electrodynamics of moving bodies, Minkowski spacetime, Einstein's quest for a theory of gravity, gravitational geometry, the concept of simultaneity, time and causality and other topics. An important Appendix -- designed to define spacetime curvature -- considers differentiable manifolds, fiber bundles, linear connections and useful formulae. Relativity continues to be a major focus of interest for physicists, mathematicians and philosophers of science. This highly regarded work offers them a rich, "historico-critical" exposition -- emphasizing geometrical ideas -- of the elements of the Special and General Theory of Relativity.
Author: Kai S Lam
Publisher: World Scientific Publishing Company
ISBN: 9813107480
Category : Science
Languages : en
Pages : 458
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Book Description
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: Stefano Trillo
Publisher: Springer Science & Business Media
ISBN: 9783540416531
Category : Science
Languages : en
Pages : 492
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Book Description
Soliton-based concepts open the road for newly designed laser sources, new frequency converters and high-intensity laser-material interactions. Optical solitons as stable spatial patterns of complex nonlinear systems allow for the control of the diffraction of optical beams. Solitons also prevent unwanted chaotic behavior. Thus, solitary wave physics plays a significant role from modern optical physics to optical communication, optical switching, and optical storage. The book gives an updated overview of optical solitons and can serve as a reference and guide for advanced students and scientists working in the field and related areas of science where solitons are observed.
