Displaying similar documents to “Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations”

Scattering length and capacity

M. Kac, J. M. Luttinger (1975)

Annales de l'institut Fourier

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An expression in terms of the Wiener integral for the “scattering length” is given and used to discuss the relation between this quantity and electrostatic capacity.

The radiation field is a Fourier integral operator

Antônio Sá Barreto, Jared Wunsch (2005)

Annales de l’institut Fourier

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We show that the ``radiation field'' introduced by F.G. Friedlander, mapping Cauchy data for the wave equation to the rescaled asymptotic behavior of the wave, is a Fourier integral operator on any non-trapping asymptotically hyperbolic or asymptotically conic manifold. The underlying canonical relation is associated to a ``sojourn time'' or ``Busemann function'' for geodesics. As a consequence we obtain some information about the high frequency behavior of the...

Asymptotic behavior of scattering amplitudes in semi-classical and low energy limits

Didier Robert, H. Tamura (1989)

Annales de l'institut Fourier

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We study the semi-classical asymptotic behavior as ( h → 0 ) of scattering amplitudes for Schrödinger operators - ( 1 / 2 ) h 2 Δ + V . The asymptotic formula is obtained for energies fixed in a non-trapping energy range and also is applied to study the low energy behavior of scattering amplitudes for a certain class of slowly decreasing repulsive potentials without spherical symmetry.

Recovering Asymptotics at Infinity of Perturbations of Stratified Media

Tanya Christiansen, Mark S. Joshi (2000)

Journées équations aux dérivées partielles

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We consider perturbations of a stratified medium ℝ x n - 1 × ℝ y , where the operator studied is c 2 ( x , y ) Δ . The function c is a perturbation of c 0 ( y ) , which is constant for sufficiently large | y | and satisfies some other conditions. Under certain restrictions on the perturbation c , we give results on the Fourier integral operator structure of the scattering matrix. Moreover, we show that we can recover the asymptotic expansion at infinity of c from knowledge of c 0 and the singularities of the scattering matrix at...

On solutions of the Schrödinger equation with radiation conditions at infinity : the long-range case

Yannick Gâtel, Dimitri Yafaev (1999)

Annales de l'institut Fourier

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We consider the homogeneous Schrödinger equation with a long-range potential and show that its solutions satisfying some a priori bound at infinity can asymptotically be expressed as a sum of incoming and outgoing distorted spherical waves. Coefficients of these waves are related by the scattering matrix. This generalizes a similar result obtained earlier in the short-range case.