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arXiv · 1703.03488

Quantum walks with an anisotropic coin I: spectral theory

S. Richard·A. Suzuki·R. Tiedra de Aldecoa
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Abstract

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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S. Richard, A. Suzuki, R. Tiedra de Aldecoa. 2017-03-09. Quantum walks with an anisotropic coin I: spectral theory. https://doi.org/10.1007/s11005-017-1008-1

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