标题： 普朗克扩散：安德森局域化的幽灵 显示英文标题

标题： Planckian Diffusion: The Ghost of Anderson Localization

摘要： 我们发现当随机介质开始运动时，安德森局域化不再存在，但另一种基本的量子效应——普朗克扩散$D = \alpha\hbar/m$取而代之出现，其$\alpha $的数量级为一。 普朗克扩散取代了普朗克速度极限$\tau= \alpha \hbar/k_B T,$，因为它不仅在热系统中暗示了这一关系，而且无需热平衡即可更普遍地应用。 在这里，我们建模了一个包含数千个游离杂质的动态无序系统，这些杂质具有随机的初始位置和速度。 通过逐步从零增加它们的速度，我们观察到从安德森局域化到普朗克扩散的转变，其中$\alpha$落在$0.5$到$2$的范围内。 此外，我们将安德森局域化的破坏与三个额外的不同确认案例相关联，这些案例也表现出普朗克扩散$D\sim \hbar/m$，包括一次关于固态氢的实验。 我们的发现表明，在动态无序系统中的普朗克扩散与静态无序系统中的安德森局域化一样普遍，这可能为量子输运研究提供新的见解。 显示英文摘要

摘要： We find that Anderson localization ceases to exist when a random medium begins to move, but another type of fundamental quantum effect, Planckian diffusion $D = \alpha\hbar/m$, rises to replace it, with $\alpha $ of order of unity. Planckian diffusion supercedes the Planckian speed limit $\tau= \alpha \hbar/k_B T,$ as it not only implies this relation in thermal systems but also applies more generally without requiring thermal equilibrium. Here we model a dynamic disordered system with thousands of itinerant impurities, having random initial positions and velocities. By incrementally increasing their speed from zero, we observe a transition from Anderson localization to Planckian diffusion, with $\alpha$ falling within the range of $0.5$ to $2$. Furthermore, we relate the breakdown of Anderson localization to three additional, distinctly different confirming cases that also exhibit Planckian diffusion $D\sim \hbar/m$, including one experiment on solid hydrogen. Our finding suggests that Planckian diffusion in dynamic disordered systems is as universal as Anderson localization in static disordered systems, which may shed light on quantum transport studies.