Coherent Propagation of Two Interacting Particles in a Random Potential

It is shown that in a random potential two repulsing or attracting particles can propagate coherently on a distance $l_c$ much larger than one-particle localization length $l_1$. The enhancement factor $\frac{l_c}{l_1}$ for coherent localization length is proportional to $l_1$. The connection of this problem with the superimposed band random matrices is established, and the theory developed is tested in numerical simulations with random potential models and models of quantum chaos.