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arXiv · 2004.13099

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

Miguel Ballesteros·Gerardo Franco Córdova·Hermann Schulz-Baldes
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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.

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Miguel Ballesteros, Gerardo Franco Córdova, Hermann Schulz-Baldes. 2020-04-27. Analyticity properties of the scattering matrix for matrix Schr\"odinger operators on the discrete line. https://arxiv.org/abs/2004.13099

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