Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time
Mathematical Physics
2009-11-10 v2 Analysis of PDEs
math.MP
Abstract
We prove that the scattering matrix at a fixed quasi--energy determines uniquely a time--periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time--independent case, where it was only known for bounded exponentially decreasing potentials.
Cite
@article{arxiv.math-ph/0309043,
title = {Inverse Scattering at a Fixed Quasi-Energy for Potentials Periodic in Time},
author = {Ricardo Weder},
journal= {arXiv preprint arXiv:math-ph/0309043},
year = {2009}
}
Comments
In this revised version I give a more detailed motivation of the class of potentials that I consider and I have corrected some typos