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arXiv · 2210.10596

Scattering for Schr\"{o}dinger operators with conical decay

Adam Black·Tal Malinovitch
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Abstract

We study the scattering properties of Schr\"{o}dinger operators with potentials that have short-range decay along a collection of rays in $\bbR^d$. This generalizes the classical setting of short-range scattering in which the potential is assumed to decay along \emph{all} rays. For these operators, we show that any state decomposes into an asymptotically free piece and a piece which may interact with the potential for long times. We give a microlocal characterization of the scattering states in terms of the dynamics and a corresponding description of their complement. We also show that in certain cases these characterizations can be purely spatial.

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Adam Black, Tal Malinovitch. 2022-10-19. Scattering for Schr\"{o}dinger operators with conical decay. https://doi.org/10.1016/j.jfa.2025.110831

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