Statistical properties of the first excited state of an interacting many-particle disordered system

The distribution P-1 of the first many-body excitation energy of a weakly and moderately interacting electron gas in a finite conductor (in the diffusive regime) is calculated. As the interaction is increased, P-1 crosses over from Wigner-Dyson to Poisson distributions. We characterize this transition through the inverse participation ratio in Hilbert space, and examine its manifestation in a projected two-dimensional space.