Eigenvalues and threshold rezonances of a two-dimensional split-step quantum walk with strong shift
Mathematical Physics
2023-04-07 v2 math.MP
Spectral Theory
Abstract
In this paper, we derive sufficient conditions for the localization of two-dimensional split-step quantum walks with a strong shift. For this purpose, we analyze the zero points of the function introduced by Fuda et. al. (Quantum Inf Process 16(8) 203, 2017) and make these zero points explicit. These zeros provide a concrete representation of the eigenvalues and eigenvectors of the evolution operator, and in particular, clarify where localization occurs. In addition, the eigenvalues obtained here asymptotically approach threshold resonance in special cases. We also describe the display of threshold resonances and generalized eigenfunctions.
Cite
@article{arxiv.2304.02342,
title = {Eigenvalues and threshold rezonances of a two-dimensional split-step quantum walk with strong shift},
author = {Toru Fuda and Daiju Funakawa and Satoshi Sasayama and Akito Suzuki},
journal= {arXiv preprint arXiv:2304.02342},
year = {2023}
}
Comments
14 pages