Two Interacting Particles in a Random Potential: Numerical Calculations of the Interaction Matrix Elements

Abstract

We reinvestigate the validity of mapping the problem of two onsite interacting particles in a random potential onto an effective random matrix model. To this end we study numerically how the non-interacting basis is coupled by the interaction. Our results indicate that the typical coupling matrix element decreases significantly faster with increasing single-particle localization length than is assumed in the random matrix model. This leads to a much weaker enhancement than proposed earlier. We also discuss how Imry's block-scaling picture for two interacting particles is influenced by these data.