Hyper-transport of light and stochastic acceleration by evolving disorder

In 1958, Philip Anderson argued that disorder can transform a conductor into an insulator, as multiple scattering from disorder brings transport to a complete halt. This concept, known as Anderson localization, has been tested in electronic, optical, acoustic and matter wave systems, which have all shown that disorder generally works to arrest transport. One major condition is common to all work on Anderson localization: for localization to take place, the underlying potential must be constant in time (frozen). Otherwise, if the disorder is dynamically evolving, localization breaks down and diffusive transport is expected to prevail. However, it seems natural to ask: can disorder increase the transport rate beyond diffusion, possibly even beyond ballistic transport? Here, we use a paraxial optical setting as a model system, and demonstrate experimentally and numerically that an evolving random potential gives rise to stochastic acceleration, which causes an initial wave packet to expand at a rate faster than ballistic, while its transverse momentum spectrum continuously expands. We discuss the universal aspects of the phenomenon relevant for all wave systems containing disorder.