Spectral approximation for ergodic CMV operators with an application to quantum walks

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:467

Article

Fillman, Jake¹  Ong, Darren C.²  VandenBoom, Tom³ 

[1] Virginia Tech, Math, MC0123,225 Stanger St, Blacksburg, VA 24061 USA

[2] Xiamen Univ Malaysia, Jalan Sunsuria, Sepang 43900, Selangor Darul, Malaysia

[3] Rice Univ, 6100 Main St,MS 136, Houston, TX 77005 USA

关键词: Spectral theory;    Quantum walks;    CMV operators;   

DOI  :  10.1016/j.jmaa.2018.06.056

来源: Elsevier

【 摘 要 】

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 Schrodinger 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free