  We study quantum enhancement of transport in open systems in the presence of
disorder and dephasing. Quantum coherence effects may significantly enhance
transport in open systems even in the deep classical regime (where the
decoherence rate is greater than the inter-site hopping amplitude), as long as
the disorder is sufficiently strong. When the strengths of disorder and
dephasing are fixed, there is an optimal opening strength at which the coherent
transport enhancement is optimized. Analytic results are obtained in two simple
paradigmatic tight-binding models of large systems: the linear chain and the
fully connected network. The physical behavior is also reflected in the FMO
photosynthetic complex, which may be viewed as intermediate between these
paradigmatic models.
