Mesoscopic dynamical echo in quantum dots

The time evolution of a wave packet within a disordered quantum dot is investigated. It is shown that although the disorder-averaged electron density is nearly homogeneous at times of the order of the diffusive time across the dot, at larger times there is a remarkable evolution towards a state with incrasing correlation with the original state i.e., an echo appears). At long times compared to the inverse mean level spacing the density distirubiton becomes time independent and preserves a memory of the original state. These effects are shown to reveal themselves in the relaxation of current through a quantum dot weakly coupled to reservoirs.