Many-body spectral statistics of interacting fermions

We have studied the appearance of chaos in the many-body spectrum of interacting Fermions. The coupling of a single state to the Fermi sea is considered. This state is coupled to a hierarchy of states corresponding to one or several particle-hole excitations. We have considered various couplings between two successive generations of this hierarchy and determined under which conditions this coupling can lead to Wigner-Dyson correlations. We have found that the cross-over from a Poisson to a Wigner distribution is characterized not only by the ratio V/Delta(c), but also by the ratio Delta(c)/delta. V is the typical interaction matrix element, delta is the energy distance between many-body states and Delta(c) is the distance between many-body states coupled by the interaction.