Quantum walks with an anisotropic coin I: spectral theory

Autor:	Richard, S., Suzuki, A., de Aldecoa, R. Tiedra
Rok vydání:	2017
Předmět:	Mathematical Physics Mathematics - Spectral Theory
Druh dokumentu:	Working Paper
DOI:	10.1007/s11005-017-1008-1
Popis:	We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we determine the essential spectrum of U, we show the existence of locally U-smooth operators, we prove the discreteness of the eigenvalues of U outside the thresholds, and we prove the absence of singular continuous spectrum for U. Our analysis is based on new commutator methods for unitary operators in a two-Hilbert spaces setting, which are of independent interest. Comment: 26 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.03488 Zobrazit plný text záznamu View this record from Arxiv