2 INTERACTING PARTICLES IN A RANDOM POTENTIAL - MAPPING ONTO ONE-PARAMETER LOCALIZATION THEORIES WITHOUT INTERACTION

We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishi ng suitable correspondences we demonstrate that both cases can be desc ribed in terms familiar from theories of noninteracting particles. In particular, these two cases are shown to be controlled by a single sca ling variable, namely the pair conductance g(2). For an attractive or repulsive Hubbard interaction and starting from a certain effective Ha miltonian we derive a supersymmetric nonlinear a model. Its action tur ns out to be closely related to the one found by Efetov for noninterac ting electrons in disordered metals. This enables us to describe the d iffusive motion of the particle pair on scales exceeding the one-parti cle localization length L(1) and to discuss the corresponding level st atistics. For tightly bound pairs in one dimension, on the other hand, we follow early work by Dorokhov and exploit the analogy with the tra nsfer matrix approach to quasi-1d conductors. Extending our study to M particles we obtain a M-particle localization length scaling like the Mth power of the one-particle localization length.