Memory formalism for quantum control of dynamic localization

An exact evaluation of memory functions to describe dynamic localization an d excitation transfer in a small quantum system is provided to clarify the connection between two recently reported phenomena, one in quantum optics a nd the other in condensed matter physics. The possibility of quantum contro l on the basis of the calculation, with relevance to systems as widely diff erent as electrons in a crystal, atoms interacting with light, spins in cro ssed magnetic fields, and Bose condensates falling in a gravitation field, is briefly mentioned. The connection to the interacting electron-phonon sys tem and to nonlinear Schroedinger equations is pointed out.