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Mathematical theory of scattering resonances, Dyatlov, Semyon Zworski, Maciej


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Автор: Dyatlov, Semyon Zworski, Maciej
Название:  Mathematical theory of scattering resonances
ISBN: 9781470443665
Издательство: Mare Nostrum (Eurospan)
Классификация:


ISBN-10: 147044366X
Обложка/Формат: Hardback
Страницы: 631
Вес: 1.32 кг.
Дата издания: 30.09.2019
Серия: Graduate studies in mathematics
Язык: English
Размер: 189 x 265 x 40
Читательская аудитория: Professional and scholarly
Ключевые слова: Differential calculus & equations,Mathematical physics
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Поставляется из: Англии
Описание: 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 Greens 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 $0$ or $\frac14$. 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.
Дополнительное описание: Differential calculus and equations|Mathematical physics


Distribution of Resonances in Scattering by Thin Barriers

Автор: Jeffrey Galkowski
Название: Distribution of Resonances in Scattering by Thin Barriers
ISBN: 1470435721 ISBN-13(EAN): 9781470435721
Издательство: Mare Nostrum (Eurospan)
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Цена: 83160.00 T
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Описание: Studies high energy resonances for the operators $-\Delta_{\partial\Omega,\delta}:=-\Delta \delta_{\partial\Omega}\otimes V\quad \textrm{and}\quad -\Delta_{\partial\Omega,\delta`}:=-\Delta \delta_{\partial\Omega}`\otimes V\partial_\nu$ where $\Omega\subset{\mathbb{R}}^{d}$ is strictly convex with smooth boundary.

Nonlinear Equations with Small Parameter: Volume I: Oscillations and resonances

Автор: Sergey G. Glebov, Oleg M. Kiselev, Nikolai N. Tark
Название: Nonlinear Equations with Small Parameter: Volume I: Oscillations and resonances
ISBN: 3110335549 ISBN-13(EAN): 9783110335545
Издательство: Walter de Gruyter
Цена: 148700.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This two-volume monograph presents new methods of construction of global asymptotics of solutions to nonlinear equations with small parameter. These allow one to match the asymptotics of various properties with each other in transition regions and to get unified formulas for the connection of characteristic parameters of approximate solutions. This approach underlies modern asymptotic methods and gives a deep insight into crucial nonlinear phenomena in the natural sciences. These include the outset of chaos in dynamical systems, incipient solitary and shock waves, oscillatory processes in crystals, engineering applications, and quantum systems. Apart from being of independent interest, such approximate solutions serve as a foolproof basis for testing numerical algorithms. This first volume presents asymptotic methods in oscillation and resonance problems described by ordinary differential equations, whereby the second volume will be devoted to applications of asymptotic methods in waves and boundary value problems. Contents Asymptotic expansions and series Asymptotic methods for solving nonlinear equations Nonlinear oscillator in potential well Autoresonances in nonlinear systems Asymptotics for loss of stability Systems of coupled oscillators

Resonances in the Earth-Ionosphere Cavity

Автор: A.P. Nickolaenko; M. Hayakawa
Название: Resonances in the Earth-Ionosphere Cavity
ISBN: 9048160774 ISBN-13(EAN): 9789048160778
Издательство: Springer
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Цена: 214280.00 T
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Описание: Attention is given to the discussion and interpretation of formal and experimental data and their links to global atmospheric conditions such as the dynamics of global thunderstorm activity, variations of the effective height of the lower ionosphere, etc.

Symmetries, Topology and Resonances in Hamiltonian Mechanics

Автор: Valerij V. Kozlov; S.V. Bolotin; Yu. Fedorov; D. T
Название: Symmetries, Topology and Resonances in Hamiltonian Mechanics
ISBN: 3642783953 ISBN-13(EAN): 9783642783951
Издательство: Springer
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Цена: 83850.00 T
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Описание: John Hornstein has written about the author`s theorem on nonintegrability of geodesic flows on closed surfaces of genus greater than one: "Here is an example of how differential geometry, differential and algebraic topology, and Newton`s laws make music together" (Amer.

Resonances

Автор: Erkki Br?ndas; Nils Elander
Название: Resonances
ISBN: 3662137259 ISBN-13(EAN): 9783662137253
Издательство: Springer
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Цена: 104480.00 T
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Описание: Within the Schrodinger picture in this volume are collected the various theoretical and mathematical treatments of scattering together with a host of reviews of its applications to atomic and nuclear physics, to surface physics and chemistry, for example trapping of atoms on surfaces, and to amorphous condensed systems.

Special Issue on Nucleon Resonances

Автор: Elena Santopinto; RALF GOTHE; Viktor I. Mokeev
Название: Special Issue on Nucleon Resonances
ISBN: 3709148707 ISBN-13(EAN): 9783709148709
Издательство: Springer
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Цена: 69870.00 T
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Inverse Obstacle Scattering with Non-Over-Determined Scattering Data

Автор: Alexander G. Ramm
Название: Inverse Obstacle Scattering with Non-Over-Determined Scattering Data
ISBN: 1681735903 ISBN-13(EAN): 9781681735900
Издательство: Mare Nostrum (Eurospan)
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Цена: 57290.00 T
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Описание: Kalman J. Kaplan and Paul Cantz offer a biblically-based approach to suicide prevention, designed to overcome suicidogenic patterns in fourteen patients fitting into seven Graeco-Roman suicidal syndromes. Kaplan and Cantz use biblical narratives alongside an in-depth positive psychology, aimed at promoting life instead of simply preventing suicide.

Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes

Автор: Thierry Daude, Francois Nicoleau
Название: Direct and Inverse Scattering at Fixed Energy for Massless Charged Dirac Fields by Kerr-Newman-de Sitter Black Holes
ISBN: 1470423766 ISBN-13(EAN): 9781470423766
Издательство: Mare Nostrum (Eurospan)
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Цена: 74850.00 T
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Описание: Examines the direct and inverse scattering theory at fixed energy for massless charged Dirac fields evolving in the exterior region of a Kerr-Newman-de Sitter black hole. The authors establish the existence and asymptotic completeness of time-dependent wave operators associated to our Dirac fields.

Inverse Obstacle Scattering with Non-Over-Determined Scattering Data

Автор: Ramm Alexander G.
Название: Inverse Obstacle Scattering with Non-Over-Determined Scattering Data
ISBN: 1681735881 ISBN-13(EAN): 9781681735887
Издательство: Mare Nostrum (Eurospan)
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Цена: 36030.00 T
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Описание:

The inverse obstacle scattering problem consists of finding the unknown surface of a body (obstacle) from the scattering (;;), where (;;) is the scattering amplitude; is the direction of the scattered, incident wave, respectively, is the unit sphere in the ℝ3 and k > 0 is the modulus of the wave vector.

The scattering data is called non-over-determined if its dimensionality is the same as the one of the unknown object. By the dimensionality one understands the minimal number of variables of a function describing the data or an object. In an inverse obstacle scattering problem this number is 2, and an example of non-over-determined data is (): = (;₀;₀). By sub-index 0 a fixed value of a variable is denoted.

It is proved in this book that the data (), known for all in an open subset of , determines uniquely the surface and the boundary condition on . This condition can be the Dirichlet, or the Neumann, or the impedance type.

The above uniqueness theorem is of principal importance because the non-over-determined data are the minimal data determining uniquely the unknown . There were no such results in the literature, therefore the need for this book arose. This book contains a self-contained proof of the existence and uniqueness of the scattering solution for rough surfaces.


Grassmannian Geometry of Scattering Amplitudes

Автор: Arkani-Hamed
Название: Grassmannian Geometry of Scattering Amplitudes
ISBN: 1107086582 ISBN-13(EAN): 9781107086586
Издательство: Cambridge Academ
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Цена: 72870.00 T
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Описание: An essential resource examining the ongoing revolution in our understanding of perturbative quantum field theory and its connection to Grassmannian geometry. This book outlines the foundations of this important new formulation, with a self-contained and authoritative analysis of its application to planar maximally supersymmetric Yang-Mills theory.


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