Time-dependent manifestations of quantum chaos.

Abstract

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)=\ensuremath{\Vert}〈\ensuremath{\psi}(0)\ensuremath{\Vert}\ensuremath{\psi}(t)〉${\mathrm{\ensuremath{\Vert}}}^{2}$, 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.