Absence of singular continuous spectra and embedded eigenvalues for one dimensional quantum walks with general long-range coins
Abstract
This paper is a continuation of the paper 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 MSSSSdis.
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