Planckian diffusion: the ghost of Anderson localization

In static disordered media, Anderson localization leads to the halt of diffusion of waves. But what happens when these impurities are dynamical, or at least some of them are in motion? Here we report that slowly moving disorder results in Planckian diffusion in our numerical simulations. In other words, the wavepacket spreading occurs at a rate only governed by fundamental constants. Remarkably, the diffusion coefficient hovers near the Planckian rate across a broad range of impurity speeds, even when only a small fraction of impurities are mobile. Planckian diffusion is therefore the natural outcome in disordered systems with randomly moving impurities, marking a universal regime emerging from broken Anderson localization. For Maxwell distribution of impurity velocities, we further find that the diffusion rate remains robust over a wide temperature range down to 1 Kelvin. This kind of transient localization could offer an alternative explanation for the linear-in-temperature resistivity widely observed in strange metals.