Transport efficiency in topologically disordered networks with environmentally induced diffusion

We study transport in topologically disordered networks that are subjected to an environment that induces classical diffusion. The dynamics is phenomenologically described within the framework of the recently introduced quantum stochastic walk, allowing to study the crossover between coherent transport and purely classical diffusion. We find that the coupling to the environment removes all effects of localization and quickly leads to classical transport. Furthermore, we find that on the level of the transport efficiency, the system can be well described by reducing it to a two-node network (a dimer).