Planckian Diffusion: What Becomes of Anderson Localization

What happens when a random medium hosting an Anderson localized quantum particle starts to evolve in time? The subtle phase coherence leading to Anderson localization requires time to establish, and if the medium has changed enough in that time, the localization will be broken. Our finding is that over very wide ranges of parameters, the resulting diffusion is Planckian, D = hbar/m, depending only on Planck’s constant and effective mass, and independent of particle-substrate interaction strength, temperature (if applicable), substrate autocorrelation properties. In a thermal system, Planckian diffusion implies the Planckian speed limit to rate processes, but it is more general. We discuss the reasons as well as the implications of these results, for example for resistivity becoming nearly perfectly linear in temperature.