The work deals with two of the most fundamental phenomena of condensed matter: interaction and disorder. Think about ultra-cold atomic gases. One atom from the gas is a quantum particle, and thus a quantum wave as well, which has both amplitude and phase. When such quantum particles, i.e. waves fail to propagate in a disordered medium, they get trapped and come to a complete halt. This destructive interference of propagating waves is Anderson localization.
Microscopic particles, described by quantum mechanics, interact when approaching each other. The presence of interaction, at least initially, destroys localization in a cloud of quantum particles, and allows the cloud to escape and smear out, though very slowly and subdiffusively. When atoms interact (collide) they exchange not only energy and momentum, but change their phases as well. The interaction destroys regular wave patterns, leading to the loss of the phase information. As time goes on the cloud spreads and thins out.
Hot debates over the past decade were devoted to the question whether the process will stop because the effective strength of interaction becomes too low, or not.
... quantum particles continue to spread even when particle to particle interactions originally deemed to be the activator of the spreading, exert almost no strength.