Semi-classical Analysis For Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition)

Semi-classical Analysis For Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition) PDF

Author: Remi Carles

Publisher: World Scientific

Published: 2020-10-05

Total Pages: 367

ISBN-13: 9811227926

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The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent.Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schrödinger equations in negative order Sobolev spaces.The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform.

Semi-classical Analysis for Nonlinear Schrödinger Equations

Semi-classical Analysis for Nonlinear Schrödinger Equations PDF

Author: Rémi Carles

Publisher: World Scientific Publishing Company

Published: 2020-09-29

Total Pages: 0

ISBN-13: 9789811227905

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The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent. Compared with the first edition, the first part is enriched by a new section on multiphase expansions in the case of weakly nonlinear geometric optics, and an application related to this study, concerning instability results for nonlinear Schrdinger equations in negative order Sobolev spaces. The third part is an overview of results concerning nonlinear effects in the propagation of coherent states, in the case of a power nonlinearity, and in the richer case of Hartree-like nonlinearities. It includes explicit formulas of an independent interest, such as generalized Mehler's formula, generalized lens transform.

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154)

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (AM-154) PDF

Author: Spyridon Kamvissis

Publisher: Princeton University Press

Published: 2003-09-07

Total Pages: 281

ISBN-13: 069111482X

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Providing an asymptotic analysis via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime, this text exploits complete integrability to establish pointwise asymptotics for this problem's solution.

Semiclassical Analysis

Semiclassical Analysis PDF

Author: Maciej Zworski

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 448

ISBN-13: 0821883208

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"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.

Condensed Matter Field Theory

Condensed Matter Field Theory PDF

Author: Alexander Altland

Publisher: Cambridge University Press

Published: 2010-03-11

Total Pages: 785

ISBN-13: 0521769752

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This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Coherent States and Applications in Mathematical Physics

Coherent States and Applications in Mathematical Physics PDF

Author: Didier Robert

Publisher: Springer Nature

Published: 2021-05-25

Total Pages: 577

ISBN-13: 3030708454

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This second edition of the outstanding monograph on coherent states by Combescure and Robert published in 2012 is enriched with figures, historical information and numerical simulations and enlarged with five new chapters presenting important rigorous results obtained in the recent years. The new chapters include various applications such as to the time dependent Schroedinger equation and the Ehrenfest time, to the growth of norms and energy exchanges, to chaotic systems and classical systems with quantum ergodic behavior, and to open quantum systems, and to adiabatic decoupling for multicomponent systems Overall, this book presents the various types of coherent states introduced and studied in the physics and mathematics literature and describes their properties together with application to quantum physics problems. It is intended to serve as a compendium on coherent states and their applications for physicists and mathematicians, stretching from the basic mathematical structures of generalized coherent states in the sense of Perelomov via the semiclassical evolution of coherent states to various specific examples of coherent states (hydrogen atom, quantum oscillator, etc.). It goes beyond existing books on coherent states in terms of a rigorous mathematical framework

Quirky Quantum Concepts

Quirky Quantum Concepts PDF

Author: Eric L. Michelsen

Publisher: Springer Science & Business Media

Published: 2014-02-04

Total Pages: 361

ISBN-13: 1461493056

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Quirky Quantum Concepts explains the more important and more difficult concepts in theoretical quantum mechanics, especially those which are consistently neglected or confusing in many common expositions. The emphasis is on physical understanding, which is necessary for the development of new, cutting edge science. In particular, this book explains the basis for many standard quantum methods, which are too often presented without sufficient motivation or interpretation. The book is not a simplification or popularization: it is real science for real scientists. Physics includes math, and this book does not shy away from it, but neither does it hide behind it. Without conceptual understanding, math is gibberish. The discussions here provide the experimental and theoretical reasoning behind some of the great discoveries, so the reader may see how discoveries arise from a rational process of thinking, a process which Quirky Quantum Concepts makes accessible to its readers. Quirky Quantum Concepts is therefore a supplement to almost any existing quantum mechanics text. Students and scientists will appreciate the combination of conversational style, which promotes understanding, with thorough scientific accuracy.

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