Mathematical Theory Of Scattering Resonances
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Mathematical Theory Of Scattering Resonances
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Author : Semyon Dyatlov
language : en
Publisher:
Release Date : 2019
Mathematical Theory Of Scattering Resonances written by Semyon Dyatlov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Frequencies of oscillating systems categories.
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.
Mathematical Theory Of Scattering Resonances
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Author : Semyon Dyatlov
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-10
Mathematical Theory Of Scattering Resonances written by Semyon Dyatlov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-10 with Mathematics categories.
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.
Theory Of Resonances
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Author : V.I. Kukulin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Theory Of Resonances written by V.I. Kukulin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
Semiclassical Analysis
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Author : Maciej Zworski
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Semiclassical Analysis written by Maciej Zworski and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
"...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Schr Dinger Operators
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Author : Hans L. Cycon
language : en
Publisher: Springer
Release Date : 2009-08-19
Schr Dinger Operators written by Hans L. Cycon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-19 with Science categories.
A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it also helps to deepen our insight into global differential geometry. This monograph written for both graduate students and researchers summarizes and synthesizes the theory of Schrödinger operators emphasizing the progress made in the last decade by Lieb, Enss, Witten and others. Besides general properties, the book covers, in particular, multiparticle quantum mechanics including bound states of Coulomb systems and scattering theory, quantum mechanics in constant electric and magnetic fields, Schrödinger operators with random and almost periodic potentials and, finally, Schrödinger operator methods in differential geometry to prove the Morse inequalities and the index theorem.
Ricci Flow And The Sphere Theorem
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Author : Simon Brendle
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Ricci Flow And The Sphere Theorem written by Simon Brendle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
Deals with the Ricci flow, and the convergence theory for the Ricci flow. This title focuses on preserved curvature conditions, such as positive isotropic curvature. It is suitable for graduate students and researchers.
Microlocal Analysis Sharp Spectral Asymptotics And Applications Iii
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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-12
Microlocal Analysis Sharp Spectral Asymptotics And Applications Iii written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Mathematics categories.
The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the methods developed in Volumes I and II are applied to the Schrödinger and Dirac operators in smooth settings in dimensions 2 and 3.
Microlocal Analysis Sharp Spectral Asymptotics And Applications I
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Author : Victor Ivrii
language : en
Publisher: Springer Nature
Release Date : 2019-09-12
Microlocal Analysis Sharp Spectral Asymptotics And Applications I written by Victor Ivrii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-12 with Mathematics categories.
The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schrödinger operator, miscellaneous problems, and multiparticle quantum theory. In this volume the general microlocal semiclassical approach is developed, and microlocal and local semiclassical spectral asymptotics are derived.
Introduction To Spectral Theory
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Author : P.D. Hislop
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Spectral Theory written by P.D. Hislop and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.