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Quantum transport in disordered systems is studied using a polaron-basedmaster equation. The polaron approach is capable of bridging the results fromthe coherent band-like transport regime governed by the Redfield equation toincoherent hopping transport in the classical regime. A non-monotonicdependence of the diffusion coefficient is observed both as a function oftemperature and system-phonon coupling strength. In the band-like transportregime, the diffusion coefficient is shown to be linearly proportional to thesystem-phonon coupling strength, and vanishes at zero coupling due to Andersonlocalization. In the opposite classical hopping regime, we correctly recoverthat the dynamics are described by the Fermi's Golden Rule (FGR) and establishthat the scaling of the diffusion coefficient depends on the phonon bathrelaxation time. In both the hopping and band-like transport regimes, it isdemonstrated that at low temperature the zero-point fluctuations of the bathlead to non-zero transport rates, and hence a finite diffusion constant.Application to rubrene and other organic semiconductor materials shows a goodagreement with experimental mobility data.

Coherent quantum transport in disordered systems: A unified polaron treatment of hopping and band-like transport