Two interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states

For two particles in a disordered chain of length L with on-site interactio n ii, a duality transformation maps the behavior at weak interaction onto t he behavior at strong interaction. Around the fixed point of this transform ation, the interaction yields a maximum mixing of the orle body states. Whe n L approximate to L-1 (the one particle localization length), this mixing results in weak chaos accompanied by: multifractal wave functions and criti cal spectral statistics, as in the one particle problem at the mobility edg e or in certain pseudo-integrable billiards. In one dimension, a local inte raction can only yield this weak chaos hut carl never drive the two particl e system to full chaos with Wigner-Dyson statistics.