  We develop a mechanism for the controlled conversion of ballistic to
diffusive motion and vice versa. This process takes place at the interfaces of
domains with different time-dependent forces in lattices of laterally
oscillating barrier potentials. As a consequence long-time transient
oscillations of the particle density are formed which can be converted to
permanent density waves by an appropriate tuning of the driving forces. The
proposed mechanism opens the perspective of an engineering of the
nonequilibrium dynamics of particles in inhomogeneously driven lattices.
