Two interacting particles in a random potential : The random matrix model

We reinvestigate the validity of mapping the problem of two onsite interacting particles in a random potential onto an eeective random matrix model. To this end we rst study numerically how the non-interacting basis is coupled by the interaction. Our results indicate that the typical coupling matrix element decreases signiicantly faster with increasing single-particle localization length than is assumed in the random matrix model. We further show that even for models where the dependency of the coupling matrix element on the single-particle localization length is correctly described by the corresponding random matrix model its predictions for the localization length can be qualitatively incorrect. These results indicate that the mapping of an interacting random system onto an eeective random matrix model is potentially dangerous. We also discuss how Imry's block-scaling picture for two interacting particles is innuenced by the above arguments.