Quasi-ballistic evolution of a quantum particle in a random potential with arbitrary correlation time

The evolution of the mean kinetic energy and of the mean square displacement of a quantum particle in a time-dependent random potential is studied by perturbation theory in the near ballistic regime. Convenient general formulas are derived for an arbitrary correlation time, τ, of the disorder. These formulas are studied analytically near the limit of perfect dynamic disorder (τ=0) and for static disorder (τ=∞), where detailed comparison is made with earlier results. This work is the first to relate the limits of perfect dynamic disorder and of static disorder via a unified treatment for finite τ.