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.