Absence of singular continuous spectra and embedded eigenvalues for one dimensional quantum walks with general long-range coins
Mathematical Physics
2021-09-27 v3 Classical Analysis and ODEs
math.MP
Spectral Theory
Abstract
This paper is a continuation of the paper \cite{W} by the third author, which studied quantum walks with special long-range perturbations of the coin operator. In this paper, we consider general long-range perturbations of the coin operator and prove the non-existence of a singular continuous spectrum and embedded eigenvalues. The proof relies on the construction of generalized eigenfunctions (Jost solutions) which was studied in the short-range case in \cite{MSSSSdis}.
Keywords
Cite
@article{arxiv.2007.12832,
title = {Absence of singular continuous spectra and embedded eigenvalues for one dimensional quantum walks with general long-range coins},
author = {Masaya Maeda and Akito Suzuki and Kazuyuki Wada},
journal= {arXiv preprint arXiv:2007.12832},
year = {2021}
}
Comments
20 pages, 7 figures, Major revised