Physics – Quantum Physics
Scientific paper
2010-04-29
Phys. Rev. E 82, 031122 (2010)
Physics
Quantum Physics
8 pages, 4 figures
Scientific paper
10.1103/PhysRevE.82.031122
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-Andr\'e model describing the one-dimensional tight-binding model with a quasi-periodic 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.
Katsura Hosho
Shikano Yutaka
No associations
LandOfFree
Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-386831