SPARSE-RANDOM-MATRIX CONFIGURATIONS FOR 2 OR 3 INTERACTING ELECTRONS IN A RANDOM POTENTIAL

We investigate the random-matrix configurations for two or three inter acting electrons in one-dimensional disordered systems. In a suitable noninteracting localized electron basis we obtain a sparse random matr ix with very long tails which is different from the superimposed rando m-band-matrix description usually thought to be valid. The number of n onzero off-diagonal matrix elements decays very weakly from the matrix diagonal and their distribution is a Lorentzian having long tails. Th e corresponding random matrix for three interacting electrons is simil ar but even more sparse.