Spectral Approximation for Ergodic CMV Operators with an Application to Quantum Walks
Mathematical Physics
2017-12-14 v1 math.MP
Spectral Theory
Abstract
We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices. We proceed by proving several variational estimates on the measure of the spectrum and the vanishing set of the Lyapunov exponent for CMV matrices, which represent CMV analogues of results obtained for Schr\"odinger operators due to Y.\ Last in the early 1990s. Having done so, we combine those estimates with results from inverse spectral theory to obtain purely absolutely continuous spectrum.
Keywords
Cite
@article{arxiv.1712.04620,
title = {Spectral Approximation for Ergodic CMV Operators with an Application to Quantum Walks},
author = {Jake Fillman and Darren C. Ong and Tom Vandenboom},
journal= {arXiv preprint arXiv:1712.04620},
year = {2017}
}
Comments
17 pages