  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.
