Eur. Phys. J. B 10, 149-158 (1999)
https://doi.org/10.1007/s100510050838

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

¹ CEA, Service de Physique de l'État Condensé, Centre d'Études de Saclay, 91191 Gif-sur-Yvette Cedex, France
² Laboratoire de Physique de la Matière Condensée (UMR 6622 du CNRS) , Université de Nice-Sophia Antipolis, Parc Valrose, BP 71, 06108 Nice Cedex 2, France

Corresponding author: ^a pichard@spec.saclay.cea.fr

Received: 24 August 1998
Published online: 15 July 1999

Abstract

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.