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Nonlinear Poisson Brackets

Author : Mikhail Vladimirovich Karasev,Viktor Pavlovich Maslov,V. P. Maslov
Publisher : American Mathematical Soc.
Release : 1993
Category : Mathematics
ISBN : 0821845969

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Book Nonlinear Poisson Brackets Description/Summary:

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

Nonlinear Poisson Brackets

Author : Mihail Vladimirovi_ Karasev,Viktor Pavlovi_ Maslov,American Mathematical Society
Publisher : American Mathematical Soc.
Release : 2012-06-06
Category : Uncategorized
ISBN : 9780821887967

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Book Nonlinear Poisson Brackets Description/Summary:

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to describe in detail the new objects that appear in the solution of these problems. Many ideas of algebra, modern differential geometry, algebraic topology, and operator theory are synthesized here. The authors prove all statements in detail, thus making the book accessible to graduate students.

Nonlinear poisson brackets

Author : Pantelis Andrea Damianou
Publisher : Unknown
Release : 2022-06-29
Category : Uncategorized
ISBN : OCLC:1090664047

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Book Nonlinear poisson brackets Description/Summary:

Hamiltonian Mechanics of Gauge Systems

Author : Lev V. Prokhorov,Sergei V. Shabanov
Publisher : Cambridge University Press
Release : 2011-09-22
Category : Science
ISBN : 9781139500906

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Book Hamiltonian Mechanics of Gauge Systems Description/Summary:

The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

Coherent Transform, Quantization and Poisson Geometry

Author : Mikhail Vladimirovich Karasev
Publisher : American Mathematical Soc.
Release : 1998
Category : Mathematics
ISBN : 0821811789

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Book Coherent Transform, Quantization and Poisson Geometry Description/Summary:

This volume contains three extensive articles written by Karasev and his pupils. The topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. The articles contain many examples (including from physics) and complete proofs.

Fluctuational Effects in the Dynamics of Liquid Crystals

Author : E.I. Kats,V.V. Lebedev
Publisher : Springer Science & Business Media
Release : 2012-12-06
Category : Science
ISBN : 9781461243328

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Book Fluctuational Effects in the Dynamics of Liquid Crystals Description/Summary:

Liquid crystals, widely used in displays for electronic equipment and other applications, have highly unusual properties arising from the anisotropy of their molecules. It appears that some aspects of the fluid dynamics of liquid crystals, such as their viscosity, can be understood only by considering the role played by thermal fluctuations. In order to provide a theoretical framework for understanding the experimental results, the authors devote a large part of the book to a derivation of the nonlinear dynamic equations and to a discussion of linearized equations for the various types of liquid crystals. The diagrammatic and other techniques they use are of general use in condensed matter physics, and this exposition should thus be of interest to all condensed-matter theorists.

Library of Congress Subject Headings

Author : Library of Congress. Cataloging Policy and Support Office
Publisher : Unknown
Release : 2009
Category : Subject headings, Library of Congress
ISBN : UOM:39015079817063

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Book Library of Congress Subject Headings Description/Summary:

Poisson Structures and Their Normal Forms

Author : Jean-Paul Dufour,Nguyen Tien Zung
Publisher : Springer Science & Business Media
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373351

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Book Poisson Structures and Their Normal Forms Description/Summary:

The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books.

Nonlinear Poisson Brackets

Author : Mikhail Vladimirovich Karasev,M. V. KARASEV;V. P. MASLOV.
Publisher : Unknown
Release : 2022-06-29
Category : Hamiltonian systems
ISBN : 1470416190

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Book Nonlinear Poisson Brackets Description/Summary:

This book deals with two old mathematical problems. The first is the problem of constructing an analog of a Lie group for general nonlinear Poisson brackets. The second is the quantization problem for such brackets in the semiclassical approximation (which is the problem of exact quantization for the simplest classes of brackets). These problems are progressively coming to the fore in the modern theory of differential equations and quantum theory, since the approach based on constructions of algebras and Lie groups seems, in a certain sense, to be exhausted. The authors' main goal is to descri.

Integration Algorithms and Classical Mechanics

Author : Jerrold E. Marsden, George W. Patrick, and William F. Shadwick
Publisher : American Mathematical Soc.
Release : 2022-06-29
Category : Mathematics
ISBN : 0821871188

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Book Integration Algorithms and Classical Mechanics Description/Summary:

Dedicated to the late Juan Carlos Simo, this volume contains the proceedings of a workshop held at the Fields Institute in October 1993. The articles focus on current algorithms for the integration of mechanical systems, from systems in celestial mechanics to coupled rigid bodies to fluid mechanics. The scope of the articles ranges from symplectic integration methods to energy-momentum methods and related themes.

Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances

Author : Anonim
Publisher : Elsevier
Release : 2007-04-03
Category : Science
ISBN : 008048946X

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Book Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances Description/Summary:

The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wave emission, the role of essentially nonlinear wave phenomena. The specificity of the book is that analytical, numerical, and experimental approaches are presented together and complement each other. Special attention is paid on explaining the methodology, e.g. multiple time-scale asymptotic expansions, averaging and removal of resonances, in what concerns theory, high-resolution finite-volume schemes, in what concerns numerical simulations, and turntable experiments with stratified fluids, in what concerns laboratory simulations. A general introduction into GFD is given at the beginning to introduce the problematics for non-specialists. At the same time, recent new results on nonlinear geostrophic adjustment, nonlinear waves, and equatorial dynamics, including some exact results on the existence of the slow manifold, wave breaking, and nonlinear wave solutions are presented for the first time in a systematic manner. · Incorporates analytical, numerical and experimental approaches in the geophysical fluid dynamics context · Combination of essentials in GFD, of the description of analytical, numerical and experimental methods (tutorial part), and new results obtained by these methods (original part) · Provides the link between GFD and mechanics (averaging method, the method of normal forms); GFD and nonlinear physics (shocks, solitons, modons, anomalous transport, periodic nonlinear waves)

Quantization of Singular Symplectic Quotients

Author : N.P. Landsman,Markus Pflaum,Martin Schlichenmaier
Publisher : Birkhäuser
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883641

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Book Quantization of Singular Symplectic Quotients Description/Summary:

This is the first exposition of the quantization theory of singular symplectic (Marsden-Weinstein) quotients and their applications to physics. The reader will acquire an introduction to the various techniques used in this area, as well as an overview of the latest research approaches. These involve classical differential and algebraic geometry, as well as operator algebras and noncommutative geometry. Thus one will be amply prepared to follow future developments in this field.

Rigid Body Dynamics

Author : Alexey Borisov,Ivan S. Mamaev
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2018-12-03
Category : Science
ISBN : 9783110544442

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Book Rigid Body Dynamics Description/Summary:

This book provides an up-to-date overview of results in rigid body dynamics, including material concerned with the analysis of nonintegrability and chaotic behavior in various related problems. The wealth of topics covered makes it a practical reference for researchers and graduate students in mathematics, physics and mechanics. Contents Rigid Body Equations of Motion and Their Integration The Euler – Poisson Equations and Their Generalizations The Kirchhoff Equations and Related Problems of Rigid Body Dynamics Linear Integrals and Reduction Generalizations of Integrability Cases. Explicit Integration Periodic Solutions, Nonintegrability, and Transition to Chaos Appendix A : Derivation of the Kirchhoff, Poincaré – Zhukovskii, and Four-Dimensional Top Equations Appendix B: The Lie Algebra e(4) and Its Orbits Appendix C: Quaternion Equations and L-A Pair for the Generalized Goryachev – Chaplygin Top Appendix D: The Hess Case and Quantization of the Rotation Number Appendix E: Ferromagnetic Dynamics in a Magnetic Field Appendix F: The Landau – Lifshitz Equation, Discrete Systems, and the Neumann Problem Appendix G: Dynamics of Tops and Material Points on Spheres and Ellipsoids Appendix H: On the Motion of a Heavy Rigid Body in an Ideal Fluid with Circulation Appendix I: The Hamiltonian Dynamics of Self-gravitating Fluid and Gas Ellipsoids

Quantization, Poisson Brackets, and Beyond

Author : Theodore Voronov,Workshop on quantization, deformations, and new homological and categorical methods in mathematical physics
Publisher : American Mathematical Soc.
Release : 2002
Category : Mathematics
ISBN : 9780821832011

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Book Quantization, Poisson Brackets, and Beyond Description/Summary:

The papers in this volume are based on talks given at the 2001 Manchester Meeting of the London Mathematical Society, which was followed by an international workshop on Quantization, Deformations, and New Homological and Categorical Methods in Mathematical Physics. Focus is on the topics suggested by the title: quantization in its various aspects, Poisson brackets and generalizations, and structures beyond'' this, including symplectic supermanifolds, operads, Lie groupoids and Lie (bi)algebroids, and algebras with $n$-ary operations. The book offers accounts of up-to-date results as well as accessible expositions aimed at a broad reading audience of researchers in differential geometry, algebraic topology and mathematical physics.

Principles of Condensed Matter Physics

Author : P. M. Chaikin,T. C. Lubensky
Publisher : Cambridge University Press
Release : 2000-09-28
Category : Science
ISBN : 0521794501

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Book Principles of Condensed Matter Physics Description/Summary:

This successful and widely-reviewed book covering the physics of condensed matter systems is now available in paperback.

Asymptotic Methods for Wave and Quantum Problems

Author : M. V. Karasev
Publisher : American Mathematical Soc.
Release : 2003
Category : Mathematics
ISBN : 0821833367

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Book Asymptotic Methods for Wave and Quantum Problems Description/Summary:

The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.

Introduction to Mechanics and Symmetry

Author : Jerrold E. Marsden,Tudor S. Ratiu
Publisher : Springer Science & Business Media
Release : 2013-03-19
Category : Science
ISBN : 9780387217925

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Book Introduction to Mechanics and Symmetry Description/Summary:

A development of the basic theory and applications of mechanics with an emphasis on the role of symmetry. The book includes numerous specific applications, making it beneficial to physicists and engineers. Specific examples and applications show how the theory works, backed by up-to-date techniques, all of which make the text accessible to a wide variety of readers, especially senior undergraduates and graduates in mathematics, physics and engineering. This second edition has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet supplements containing additional material are also available.

Statistical Physics of Liquids at Freezing and Beyond

Author : Shankar Prasad Das
Publisher : Cambridge University Press
Release : 2011-06-16
Category : Science
ISBN : 9781139500678

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Book Statistical Physics of Liquids at Freezing and Beyond Description/Summary:

Exploring important theories for understanding freezing and the liquid-glass transition, this book is useful for graduate students and researchers in soft-condensed matter physics, chemical physics and materials science. It details recent ideas and key developments, providing an up-to-date view of current understanding. The standard tools of statistical physics for the dense liquid state are covered. The freezing transition is described from the classical density functional approach. Classical nucleation theory as well as applications of density functional methods for nucleation of crystals from the melt are discussed, and compared to results from computer simulation of simple systems. Discussions of supercooled liquids form a major part of the book. Theories of slow dynamics and the dynamical heterogeneities of the glassy state are presented, as well as nonequilibrium dynamics and thermodynamic phase transitions at deep supercooling. Mathematical treatments are given in full detail so readers can learn the basic techniques.