Semi Classical Analysis For Nonlinear Schrodinger Equations Wkb Analysis Focal Points Coherent States Second Edition PDF Download
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| Author | : Remi Carles |
| Publisher | : World Scientific |
| Total Pages | : 367 |
| Release | : 2020-10-05 |
| Genre | : Mathematics |
| ISBN | : 9811227926 |
Download Semi-classical Analysis For Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition) Book in PDF, ePub and Kindle
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.
| Author | : Rémi Carles |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 0 |
| Release | : 2020-09-29 |
| Genre | : Mathematics |
| ISBN | : 9789811227905 |
Download Semi-classical Analysis for Nonlinear Schrödinger Equations Book in PDF, ePub and Kindle
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.
| Author | : Maciej Zworski |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 448 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821883208 |
Download Semiclassical Analysis Book in PDF, ePub and Kindle
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
| Author | : Alexander Altland |
| Publisher | : Cambridge University Press |
| Total Pages | : 785 |
| Release | : 2010-03-11 |
| Genre | : Science |
| ISBN | : 0521769752 |
Download Condensed Matter Field Theory Book in PDF, ePub and Kindle
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.
| Author | : |
| Publisher | : |
| Total Pages | : 1586 |
| Release | : 1991 |
| Genre | : Physics |
| ISBN | : |
Download Physics Briefs Book in PDF, ePub and Kindle
| Author | : Didier Robert |
| Publisher | : Springer Nature |
| Total Pages | : 577 |
| Release | : 2021-05-25 |
| Genre | : Science |
| ISBN | : 3030708454 |
Download Coherent States and Applications in Mathematical Physics Book in PDF, ePub and Kindle
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
| Author | : Eric L. Michelsen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 361 |
| Release | : 2014-02-04 |
| Genre | : Science |
| ISBN | : 1461493056 |
Download Quirky Quantum Concepts Book in PDF, ePub and Kindle
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.
| Author | : Hagen Kleinert |
| Publisher | : World Scientific |
| Total Pages | : 1626 |
| Release | : 2009 |
| Genre | : Business & Economics |
| ISBN | : 9814273570 |
Download Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets Book in PDF, ePub and Kindle
Topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect." "The relevance of path integrals to financial markets is discussed, and improvements of the famous Black-Scholes formula for option prices are developed which account for the fact that large market fluctuations occur much more frequently than in Gaussian distributions." --Book Jacket.
| Author | : Bei-Lok B. Hu |
| Publisher | : Cambridge University Press |
| Total Pages | : 615 |
| Release | : 2020-03-05 |
| Genre | : Science |
| ISBN | : 1108854141 |
Download Semiclassical and Stochastic Gravity Book in PDF, ePub and Kindle
The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.
| Author | : Michael Stone |
| Publisher | : Cambridge University Press |
| Total Pages | : 821 |
| Release | : 2009-07-09 |
| Genre | : Science |
| ISBN | : 1139480618 |
Download Mathematics for Physics Book in PDF, ePub and Kindle
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.
