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 L1, and the partial dephasing induced by a local interaction of strength U with another particle leading to partial delocalization over a length L2 > L1, 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 t1 necessary to propagate over L1, the interaction slows down the ballistic motion. On the contrary, after t1 the interaction favors a very slow delocalization, characterized by a log(t) spreading of the center of mass, until L2 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 . PACS. 71.10.-w Theories and models of many electron systems – 71.30.+h Metal-insulator transitions and other electronic transitions – 73.20.Jc Delocalization processes