Two interacting particles in a disordered chain III: Dynamical aspects of the interplay disorder-interaction

The interplay between the quantum interferences responsible for one particle localization over a length L-1, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L-2 > L-1, is illustrated by a study of the motion of two particles put close to each other at the initial time. Localization is reached in two steps. First, before the time t(1) necessary to propagate over L-1, the interaction slows down the ballistic motion. On the contrary, after t(1) the interaction favors a very slow delocalization, characterized by a log(t) spreading of the center of mass, until L-2 is reached. This slow motion is related to the absence of quantum chaos in this one dimensional model, the interaction being only able to induce weaker chaos with critical spectral statistics. Under appropriate initial conditions, the motion remains invariant under the duality transformation mapping the behavior at small U onto the behavior at large U.