Spectral Approximation for Ergodic CMV Operators with an Application to Quantum Walks

Autor:	Fillman, Jake, Ong, Darren C., Vandenboom, Tom
Rok vydání:	2017
Předmět:	Mathematical Physics Mathematics - Spectral Theory 47B36
Druh dokumentu:	Working Paper
Popis:	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. Comment: 17 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1712.04620 Zobrazit plný text záznamu View this record from Arxiv