Impurity-Controlled Transport within a Finite Disordered Lattice

We consider a finite disordered 1D quantum lattice with an attached impurity. We study the transport of a single electron from the impurity to the lattice at zero temperature. The transport is dominated by Anderson localization and in general it has a random character due to the lattice disorder. However we show theoretically that, by adjusting the impurity energy, the electron can attain quite regular, periodic motions. In particular, by a precise tuning of the impurity energy, the electron can be set to oscillate between the impurity and lattice sites far from the impurity, at distances larger than the Anderson localization length, and with long periods of oscillation. This phenomenon may be observable in analogous optical systems.