论文标题
Aharonov-bohm笼子中的稳健性
Robustness of Aharonov-Bohm cages in quantum walks
论文作者
论文摘要
最近显示，在某些瓷砖上存在量子步行（QW）的Aharonov-Bohm（AB）笼子 - 例如钻石链或骰子（或$ \ Mathcal {t} _3 $）晶格 - 用于适当选择硬币。在本文中，我们探测了这些AB笼子对各种扰动的鲁棒性。当笼子被破坏时，我们分析泄漏机制并表征所得的动力学。淬火障碍通常会打破笼子，并导致与安德森本地化类似的波功能的指数衰减。动态混乱或重复测量破坏了相一致性，并将QW变成具有扩散行为的经典随机行走。以特定方式组合静态和动力学障碍会导致细胞扩散与受淬火疾病分布控制的异常指数。将相互作用引入第二个助行器也可以打破笼子并恢复“分子”结合状态的弹道运动。
It was recently shown that Aharonov-Bohm (AB) cages exist for quantum walks (QW) on certain tilings -- such as the diamond chain or the dice (or $\mathcal{T}_3$) lattice -- for a proper choice of coins. In this article, we probe the robustness of these AB cages to various perturbations. When the cages are destroyed, we analyze the leakage mechanism and characterize the resulting dynamics. Quenched disorder typically breaks the cages and leads to an exponential decay of the wavefunction similar to Anderson localization. Dynamical disorder or repeated measurements destroy phase coherence and turn the QW into a classical random walk with diffusive behavior. Combining static and dynamical disorder in a specific way leads to subdiffusion with an anomalous exponent controlled by the quenched disorder distribution. Introducing interaction to a second walker can also break the cages and restore a ballistic motion for a "molecular" bound-state.
