Transport and Localization in Quantum Walks on a Random Hierarchy of Barriers
arXiv:2205.09308 · doi:10.1088/1751-8121/ac7117
Abstract
We study transport within a spatially heterogeneous one-dimensional quantum walk with a combination of hierarchical and random barriers. Recent renormalization group calculations for a spatially disordered quantum walk with a regular hierarchy of barriers alone have shown a gradual decrease in transport but no localization for increasing (but finite) barrier sizes. In turn, it is well-known that extensive random disorder in the spatial barriers is sufficient to localize a quantum walk on the line. Here we show that adding only a sparse (sub-extensive) amount of randomness to a hierarchy of barriers is sufficient to induce localization such that transport ceases. Our numerical results suggest the existence of a localization transition for a combination of both, the strength of the regular barrier hierarchy at large enough randomness as well as the increasing randomness at sufficiently strong barriers in the hierarchy.
arXiv comment9 pages, 6 figures, RevTex, accepted manuscript available online at J. Phys. A. For related information, see http://www.physics.emory.edu/faculty/boettcher/
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