Mathematical Theory Of Scattering Resonances PDF Download
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Author | : Semyon Dyatlov |
Publisher | : American Mathematical Soc. |
Total Pages | : 634 |
Release | : 2019-09-10 |
Genre | : Frequencies of oscillating systems |
ISBN | : 147044366X |
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Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical, an elegant mathematical formulation comes from considering meromorphic continuations of Green's functions. The poles of these meromorphic continuations capture physical information by identifying the rate of oscillation with the real part of a pole and the rate of decay with its imaginary part. An example from mathematics is given by the zeros of the Riemann zeta function: they are, essentially, the resonances of the Laplacian on the modular surface. The Riemann hypothesis then states that the decay rates for the modular surface are all either or . An example from physics is given by quasi-normal modes of black holes which appear in long-time asymptotics of gravitational waves. This book concentrates mostly on the simplest case of scattering by compactly supported potentials but provides pointers to modern literature where more general cases are studied. It also presents a recent approach to the study of resonances on asymptotically hyperbolic manifolds. The last two chapters are devoted to semiclassical methods in the study of resonances.
Author | : V.I. Kukulin |
Publisher | : Springer Science & Business Media |
Total Pages | : 354 |
Release | : 2013-06-29 |
Genre | : Science |
ISBN | : 9401578176 |
Download Theory of Resonances Book in PDF, ePub and Kindle
Author | : Luchezar N. Stoyanov |
Publisher | : American Mathematical Soc. |
Total Pages | : 90 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821842943 |
Download Scattering Resonances for Several Small Convex Bodies and the Lax-Phillips Conjecture Book in PDF, ePub and Kindle
This work deals with scattering by obstacles which are finite disjoint unions of strictly convex bodies with smooth boundaries in an odd dimensional Euclidean space. The class of obstacles of this type which is considered are contained in a given (large) ball and have some additional properties.
Author | : D. R. Yafaev |
Publisher | : American Mathematical Soc. |
Total Pages | : 356 |
Release | : 1992-09-09 |
Genre | : Mathematics |
ISBN | : 9780821897379 |
Download Mathematical Scattering Theory Book in PDF, ePub and Kindle
Preliminary facts Basic concepts of scattering theory Further properties of the WO Scattering for relatively smooth perturbations The general setup in stationary scattering theory Scattering for perturbations of trace class type Properties of the scattering matrix (SM) The spectral shift function (SSF) and the trace formula
Author | : Dmitri_ Rauel_evich I_Afaev |
Publisher | : American Mathematical Soc. |
Total Pages | : 370 |
Release | : 2010-03-10 |
Genre | : Mathematics |
ISBN | : 082180331X |
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The main subject of this book is applications of methods of scattering theory to differential operators, primarily the Schrodinger operator. There are two different trends in scattering theory for differential operators. The first one relies on the abstract scattering theory. The second one is almost independent of it. In this approach the abstract theory is replaced by a concrete investigation of the corresponding differential equation. In this book both of these trends are presented. The first half of this book begins with the summary of the main results of the general scattering theory of the previous book by the author, Mathematical Scattering Theory: General Theory, American Mathematical Society, 1992. The next three chapters illustrate basic theorems of abstract scattering theory, presenting, in particular, their applications to scattering theory of perturbations of differential operators with constant coefficients and to the analysis of the trace class method. In the second half of the book direct methods of scattering theory for differential operators are presented. After considering the one-dimensional case, the author returns to the multi-dimensional problem and discusses various analytical methods and tools appropriate for the analysis of differential operators, including, among others, high- and low-energy asymptotics of the Green function, the scattering matrix, ray and eikonal expansions. The book is based on graduate courses taught by the author at Saint-Petersburg (Russia) and Rennes (France) Universities and is oriented towards a reader interested in studying deep aspects of scattering theory (for example, a graduate student in mathematical physics).
Author | : Harald Friedrich |
Publisher | : Springer |
Total Pages | : 293 |
Release | : 2015-11-20 |
Genre | : Science |
ISBN | : 3662485265 |
Download Scattering Theory Book in PDF, ePub and Kindle
This corrected and updated second edition of "Scattering Theory" presents a concise and modern coverage of the subject. In the present treatment, special attention is given to the role played by the long-range behaviour of the projectile-target interaction, and a theory is developed, which is well suited to describe near-threshold bound and continuum states in realistic binary systems such as diatomic molecules or molecular ions. It is motivated by the fact that experimental advances have shifted and broadened the scope of applications where concepts from scattering theory are used, e.g. to the field of ultracold atoms and molecules, which has been experiencing enormous growth in recent years, largely triggered by the successful realization of Bose-Einstein condensates of dilute atomic gases in 1995. The book contains sections on special topics such as near-threshold quantization, quantum reflection, Feshbach resonances and the quantum description of scattering in two dimensions. The level of abstraction is kept as low as at all possible and deeper questions related to the mathematical foundations of scattering theory are passed by. It should be understandable for anyone with a basic knowledge of nonrelativistic quantum mechanics. The book is intended for advanced students and researchers, and it is hoped that it will be useful for theorists and experimentalists alike.
Author | : Philippe Briet |
Publisher | : American Mathematical Soc. |
Total Pages | : 202 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821858262 |
Download Spectral and Scattering Theory for Quantum Magnetic Systems, July 7-11, 2008, CIRM, Luminy, Marseilles, France Book in PDF, ePub and Kindle
"This volume contains the proceedings of the conference on Spectral and Scattering Theory for Quantum Magnetic Systems, which took place at CIRM, Luminy, France, in July 2008. The main purpose of this conference was to bring together a number of specialists in the mathematical modelling of magnetic phenomena in quantum mechanics, to mark the recent progress as well as to outline the future development in this area. This volume contains original results presented by some of the invited speakers and surveys on recent advances in the mathematical theory of quantum magnetic Hamiltonians. Most of the talks at the conference, as well as the articles in this volume, have been dedicated to one of the following topics: Spectral and scattering theory for magnetic Schrödinger operators ; Magnetic Pauli and Dirac operators ; Magnetic operators on manifolds ; Microlocal analysis of magnetic Hamiltonians ; Random Schrödinger operators and quantum Hall effect ; Ginsburg-Landau equation, supraconductivity, magnetic bottles ; Bose-Einstein condensate, Gross-Pitaevski equation ; Magnetic Lieb-Thirring inequalities, stability of matter."--Publisher's website.
Author | : Michael Reed |
Publisher | : Academic Press |
Total Pages | : 488 |
Release | : 1979-04-28 |
Genre | : Mathematics |
ISBN | : |
Download III: Scattering Theory Book in PDF, ePub and Kindle
Volume 3.
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 | : M. Ikawa |
Publisher | : CRC Press |
Total Pages | : 348 |
Release | : 2020-12-17 |
Genre | : Mathematics |
ISBN | : 100011709X |
Download Spectral and Scattering Theory Book in PDF, ePub and Kindle
"This useful volume, based on the Taniguchi International Workshop held recently in Sanda, Hyogo, Japan, discusses current problems and offers the mostup-to-date methods for research in spectral and scattering theory."