  Quantum transport in disordered systems is studied using a polaron-based
master equation. The polaron approach is capable of bridging the results from
the coherent band-like transport regime governed by the Redfield equation to
incoherent hopping transport in the classical regime. A non-monotonic
dependence of the diffusion coefficient is observed both as a function of
temperature and system-phonon coupling strength. In the band-like transport
regime, the diffusion coefficient is shown to be linearly proportional to the
system-phonon coupling strength, and vanishes at zero coupling due to Anderson
localization. In the opposite classical hopping regime, we correctly recover
that the dynamics are described by the Fermi's Golden Rule (FGR) and establish
that the scaling of the diffusion coefficient depends on the phonon bath
relaxation time. In both the hopping and band-like transport regimes, it is
demonstrated that at low temperature the zero-point fluctuations of the bath
lead to non-zero transport rates, and hence a finite diffusion constant.
Application to rubrene and other organic semiconductor materials shows a good
agreement with experimental mobility data.
