Abstract
As an unusual type of anomalous diffusion behavior, the (transient) superballistic transport has been experimentally observed recently but it is not well understood yet. In this paper, we investigate the white noise effect (in Markov approximation) on the quantum diffusion in 1D tight-binding model with periodic, disordered and quasi-periodic region of size L attached to two perfect lattices at both ends in which the wave packet is initially located at the center of the sublattice. We find that in some completely localized system inducing noise could delocalize the system to desirable diffusion phase. This controllable system may be used to investigate the interplay of disorder and white noise, as well as exploring exotic quantum phase.