Persistent many-body quantum echoes

Abstract

We consider quantum many-body systems evolving under a time-independent Hamiltonian H from a nonequilibrium initial state at time t=0 towards a close-to-equilibrium state at time t=τ. Subsequently, this state is slightly perturbed and finally propagated for another time period τ under the inverted Hamiltonian-H. The entire procedure may also be viewed as an imperfect time inversion or "echo dynamics." We unravel a remarkable persistence of such dynamics with respect to the observable deviations of the time-dependent expectation values from the equilibrium expectation value: For most perturbations, the deviations in the final state are essentially independent of the inversion time point τ. Our quantitative analytical predictions compare very well with exact numerical results.