论文标题
在随机的障碍层次结构上进行量子步行中的运输和定位
Transport and Localization in Quantum Walks on a Random Hierarchy of Barriers
论文作者
论文摘要
我们研究了在空间异质的一维量子步行中，并结合了分层和随机屏障的结合。仅定期屏障的常规层次结构的空间无序量子步行的最新重归其化组计算显示，运输逐渐减少，但没有增加（但有限）屏障大小的定位。反过来，众所周知，空间屏障中的广泛随机疾病足以在线上定位量子行走。在这里，我们表明，仅在障碍层次结构中添加稀疏（延伸）随机性足以诱导本地化以使运输停止。我们的数值结果表明存在与两者组合的结合，正常屏障层次结构的强度在很大的随机性以及层次结构中足够强的屏障时的随机性增加。
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.
