Resonances in finitely perturbed quantum walks, resonance expansion and generic simplicity
Kenta Higuchi, Hisashi Morioka, Etsuo Segawa · arXiv (Cornell University) · 2021
We define resonances for finitely perturbed quantum walks as poles of the scattering matrix in the lower half plane. We show a resonance expansion which describes the time evolution in terms of resonances and corresponding Jordan chains. In particular, the decay rate of the survival probability is given by the imaginary part of resonances and the multiplicity. We prove generic simplicity of the resonances, although there are quantum walks with multiple resonances.