Resonances in finitely perturbed quantum walks, resonance expansion and generic simplicity
Spectral Theory
2021-08-04 v1 Mathematical Physics
math.MP
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.2108.01345,
title = {Resonances in finitely perturbed quantum walks, resonance expansion and generic simplicity},
author = {Kenta Higuchi and Hisashi Morioka and Etsuo Segawa},
journal= {arXiv preprint arXiv:2108.01345},
year = {2021}
}
Comments
16 pages, 2 figures