  Quantum lattices are pivotal in the burgeoning fields of quantum materials
and information science. Rapid developments in microscopy and quantum
engineering allow for preparing and monitoring wave-packet dynamics on quantum
lattices with increasing spatial and temporal resolution. Motivated by these
emerging research interests, we present an analytical study of wave packet
diffusivity and diffusion length on tight-binding quantum lattices subject to
stochastic noise. Our analysis points to the crucial role of spatial coherence
and predicts a set of novel phenomena: noise can enhance the transient
diffusivity and diffusion length of sufficiently extended initial states; A
smooth Gaussian initial state spreads slower than a localized initial state; A
standing or traveling initial state with large momentum spreads faster than a
localized initial state and exhibits a noise-induced peak in the transient
diffusivity; The change in the time-dependent diffusivity and diffusion length
relative to a localized initial state follows a universal dependence on the
Gaussian width. These theoretical predictions and the underlying mechanism of
spatial coherence suggest the possibility of controlling the wave packet
dynamics on quantum lattices by spatial manipulations, which will have
implications for materials science and quantum technologies.
