Transport and localization in quantum walks on a random hierarchy of barriers. (English) Zbl 1507.81147
Summary: 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.
MSC:
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
| 81P16 | Quantum state spaces, operational and probabilistic concepts |
| 81P20 | Stochastic mechanics (including stochastic electrodynamics) |
| 82C28 | Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics |
| 82B28 | Renormalization group methods in equilibrium statistical mechanics |
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