Purely Singular Continuous Spectrum for Limit-Periodic CMV Operators with Applications to Quantum Walks
Spectral Theory
2016-10-20 v1 Functional Analysis
Abstract
We show that a generic element of a space of limit-periodic CMV operators has zero-measure Cantor spectrum. We also prove a Craig--Simon type theorem for the density of states measure associated with a stochastic family of CMV matrices and use our construction from the first part to prove that the Craig--Simon result is optimal in general. We discuss applications of these results to a quantum walk model where the coins are arranged according to a limit-periodic sequence. The key ingredient in these results is a new formula which may be viewed as a relationship between the density of states measure of a CMV matrix and its Schur function.
Keywords
Cite
@article{arxiv.1610.06159,
title = {Purely Singular Continuous Spectrum for Limit-Periodic CMV Operators with Applications to Quantum Walks},
author = {Jake Fillman and Darren C. Ong},
journal= {arXiv preprint arXiv:1610.06159},
year = {2016}
}
Comments
28 pages