Planckian Diffusion: The Ghost of Anderson Localization

Abstract: 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.