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