English

Analyticity properties of the scattering matrix for matrix Schr\"odinger operators on the discrete line

Mathematical Physics 2021-01-25 v2 math.MP

Abstract

Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schr\"odinger operator with a potential of finite support are derived. This includes a careful analysis of the band edge singularities and allows to prove a Levinson-type theorem. The main algebraic tool are the plane wave transfer matrices.

Keywords

Cite

@article{arxiv.2004.13099,
  title  = {Analyticity properties of the scattering matrix for matrix Schr\"odinger operators on the discrete line},
  author = {Miguel Ballesteros and Gerardo Franco Córdova and Hermann Schulz-Baldes},
  journal= {arXiv preprint arXiv:2004.13099},
  year   = {2021}
}

Comments

minor corrections, to appear in J. Math. Analysis and its Applications