Time-dependent manifestations of quantum chaos

We show that regular and irregular spectral statistics have direct, distinctive, and observable time-dependent manifestations in the behavior of the survival probability P(t)=‖〈ψ(0)‖ψ(t)〉${\mathrm{\Vert }}^2$, averaged over Hamiltonian ensembles and initial conditions. Specifically, systems exhibiting energy-level repulsion display characteristically strong decorrelations at short times. The proof relies solely on Liouville spectral properties of ensembles of bound quantum systems.