  We study the spreading of a quantum-mechanical wavepacket in a
one-dimensional tight-binding model with a noisy potential, and analyze the
emergence of classical diffusion from the quantum dynamics due to decoherence.
We consider a finite correlation time of the noisy environment, and treat the
system by utilizing the separation of fast (dephasing) and slow (diffusion)
processes. We show that classical diffusive behavior emerges at long times, and
we calculate analytically the dependence of the classical diffusion coefficient
on the noise magnitude and correlation time. This method provides a general
solution to this problem for arbitrary conditions of the noisy environment. The
results are relevant to a large variety of physical systems, from electronic
transport in solid state physics, to light transmission in optical devices,
diffusion of excitons, and quantum computation.
