@article{oai:nagoya.repo.nii.ac.jp:00025742, author = {Richard, Serge and Suzuki, A. and Tiedra de Aldecoa, R.}, issue = {2}, journal = {Letters in Mathematical Physics}, month = {Feb}, note = {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., ファイル公開:2019/02/01}, pages = {331--357}, title = {Quantum walks with an anisotropic coin I: spectral theory}, volume = {108}, year = {2018} }