Localization Properties of Two Interacting Electrons in a Disordered Quasi One-Dimensional Potential

We study the transport properties of two electrons in a quasi one-dimensional disordered wire. The electrons are subject to both, a disorder potential and a short range two-body interaction. Using the approach developed by Iida et al. [ Ann. Phys. (N.Y.) 200 (1990) 219 ], the supersymmetry technique, and a suitable truncation of Hilbert space, we work out the two-point correlation function in the framework of a non-linear sigma model. We study the loop corrections to arbitrary order. We obtain a remarkably simple and physically transparent expression for the change of the localization length caused by the two-body interaction.