期刊
LETTERS IN MATHEMATICAL PHYSICS
卷 108, 期 2, 页码 331-357出版社
SPRINGER
DOI: 10.1007/s11005-017-1008-1
关键词
Quantum walks; Spectral theory; Commutator methods; Unitary operators
资金
- JSPS [26707005, 26800054]
- Chilean Fondecyt Grant [1170008]
- Grants-in-Aid for Scientific Research [26707005, 26800054] Funding Source: KAKEN
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.
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