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Coherent propagation of two interacting particles in $1d$ weak randompotential is considered. An accurate estimate of the matrix element ofinteraction in the basis of localized states leads to mapping onto the relevantmatrix model. This mapping allows to clarify the mechanism of enhancement ofthe localization length which turns out to be rather different from the oneconsidered in the literature. Although the existence of enhancement istransparent, an analytical solution of the matrix model was found only for veryshort samples. For a more realistic situation numerical simulations wereperformed. The result of these simulations is consistent with l_{2}/l_1 \siml_1^{\gamma} , where $l_1$ and $l_2$ are the single and two particlelocalization lengths and the exponent $\gamma$ depends on the strength of theinteraction. In particular, in the limit of strong particle-particleinteraction there is no enhancement of the coherent propagation at all ($l_{2}\approx l_1$).Comment: 23 pages, REVTEX, 3 eps figures, improved version accepted for  publication in Phys. Rev.

Coherent propagation of interacting particles in a random potential: The mechanism of enhancement