Criteria for the onset of chaos in finite Fermi systems

The level density in a many-particle Fermi system at a given excitation energy is exponentially large with respect to the number of active particles n, and the corresponding mean level spacing D is very small. We consider the eigenstates of the system in the basis of multi-particle excited states constructed of some non-interacting single-particle orbitals. Most of the basis states are not coupled directly with each other by the two-body interaction between particles. However, if the interaction is strong enough, a regime of “complete” mixing of basis states within a certain energy interval Γ (the spreading width), or what we call “chaos”, emerges in the system. The onset of quantum chaos is determined by the following condition: V/ √ dfD > 1, where V is the root-mean-square two-body matrix element, and df is of the order of the level spacing between the 2-particle−1-hole excited states.