Crossover phenomena in the excitation statistics of disordered many-particle systems

The energy level separation distribution of a fermionic disordered many-particle system is studied. For a non-interacting system, a crossover is observed from a Wigner (GOE) distribution for the first and second excitations to a different form which depends on the number of particles for low-lying excitations and then to a Poisson distribution for high excitations. This behaviour also holds for weakly interacting systems, while for stronger interactions a transition of the high excitations to a Wigner distribution is observed.