Localization and fractality in inhomogeneous quantum walks with self-duality
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Shikano-2010-Localization and fra.pdf
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Author(s)
Shikano, Yutaka
Katsura, Hosho
Date Issued
September 2010
Journal
Physical Review E
Publisher
American Physical Society
Citation
Shikano, Yutaka, and Hosho Katsura. “Localization and fractality in inhomogeneous quantum walks with self-duality.” Physical Review E 82.3 (2010): 031122. © 2010 The American Physical Society.
Version
Final published version
Abstract
We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The models are shown to be self-dual with respect to the Fourier transform, which is analogous to the Aubry-André model describing the one-dimensional tight-binding model with a quasiperiodic potential. When the period of coin operators is incommensurate to the lattice spacing, we rigorously show that the limit distribution of the quantum walk is localized at the origin. We also numerically study the eigenvalues of the one-step time evolution operator and find the Hofstadter butterfly spectrum which indicates the fractal nature of this class of quantum walks.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.82.031122
