Interaction-induced delocalization of two particles in a random potential: Scaling properties

The localization length xi(2) for coherent propagation of two interacting particles in a random potential is studied using a novel and efficient numerical method. We find that the enhancement of xi(2) over the one-particle localization length xi(1) satisfies the scaling relation xi(2)/xi(1) = f(u/Delta(xi)) where u is the interaction strength and Delta(xi) the level spacing of a wire of length xi(1). The scaling function f is linear over the investigated parameter range. This implies that xi(2) increases faster with u than previously predicted. We also study a novel mapping of the problem to a banded-random-matrix model.