Complex translation methods and its application to resonances for quantum walks
Spectral Theory
2024-03-26 v3 Mathematical Physics
Analysis of PDEs
math.MP
Abstract
In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue of classical mechanics. Another one is a shape resonance model which is a perturbation of a quantum walk with a non-penetrable barrier.
Keywords
Cite
@article{arxiv.2307.00962,
title = {Complex translation methods and its application to resonances for quantum walks},
author = {Kenta Higuchi and Hisashi Morioka},
journal= {arXiv preprint arXiv:2307.00962},
year = {2024}
}