Propagation of singularities in many-body scattering

András Vasy

Displaying similar documents to “Propagation of singularities in many-body scattering”

Singularities of the scattering kernel for trapping obstacles

Vesselin Petkov, Latchezar Stoyanov (1996)

Annales scientifiques de l'École Normale Supérieure

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Propagation of singularities in many-body scattering in the presence of bound states

András Vasy (1999)

Journées équations aux dérivées partielles

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In these lecture notes we describe the propagation of singularities of tempered distributional solutions $u \in 𝒮^{'}$ of $(H - λ) u = 0$ , where $H$ is a many-body hamiltonian $H = Δ + V$ , $Δ \geq 0$ , $V = \sum_{a} V_{a}$ , and $λ$ is not a threshold of $H$ , under the assumption that the inter-particle (e.g. two-body) interactions $V_{a}$ are real-valued polyhomogeneous symbols of order $- 1$ (e.g. Coulomb-type with the singularity at the origin removed). Here the term “singularity” provides a microlocal description of the lack of decay at infinity. Our result is...

Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations

Tanya Christiansen, M. S. Joshi (2003)

Annales de l’institut Fourier

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The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.

Scattering matrix for asymptotically euclidean manifolds

Richard Melrose, Maciej Zworski (1994)

Journées équations aux dérivées partielles

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The resolvent for Laplace-type operators on asymptotically conic spaces

Andrew Hassell, András Vasy (2001)

Annales de l’institut Fourier

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Let $X$ be a compact manifold with boundary, and $g$ a scattering metric on $X$ , which may be either of short range or “gravitational” long range type. Thus, $g$ gives $X$ the geometric structure of a complete manifold with an asymptotically conic end. Let $H$ be an operator of the form $H = Δ + P$ , where $Δ$ is the Laplacian with respect to $g$ and $P$ is a self-adjoint first order scattering differential operator with coefficients vanishing at $\partial X$ and satisfying a “gravitational” condition. We define a symbol calculus...

Poisson relation for the scattering kernel and inverse scattering by obstacles

L. Stoyanov (1994-1995)

Séminaire Équations aux dérivées partielles (Polytechnique)

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