Localization and fractality in inhomogeneous quantum walks with self-duality.

摘要: We introduce and study a class of discrete-time quantum walks on one-dimensional lattice. In contrast to the standard homogeneous walks, coin operators are inhomogeneous depend their positions in this models. The models shown be self-dual with respect Fourier transform, which is analogous Aubry-Andre model describing tight-binding quasiperiodic potential. When period incommensurate lattice spacing, we rigorously show that limit distribution walk localized at origin. also numerically eigenvalues one-step time evolution operator find Hofstadter butterfly spectrum indicates fractal nature walks.