English

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 L3/2L^{3/2} 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