Do we understand the role of incoherent interactions in many-body physics?

Recent developments in many-body quantum chaos show that a quantum system with strong incoherent interactions can still be described with the aid of mean quasiparticle occupation numbers as in Fermi liquid theory. We use these ideas and the geometric chaoticity of angular momentum coupling to explain the predominance of ground states with zero spin and the maximum possible spin for a system of randomly interacting fermions in a rotationally invariant mean field (an analog of the Hund rule). We show that spin ordering coexists with the chaotic features of the ground-state wave functions.