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

Abstract

The localization length $ξ_2$ 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 $ξ_2$ over the one-particle localization length $ξ_1$ satisfies the scaling relation $ξ_2/ξ_1=f(u/Δ_ξ)$, where $u$ is the interaction strength and $Δ_ξ$ the level spacing of a wire of length $ξ_1$. The scaling function $f$ is linear over the investigated parameter range. This implies that $ξ_2$ increases faster with $u$ than previously predicted. We also study a novel mapping of the problem to a banded-random-matrix model.