Duality symmetries and effective dynamics in disordered hopping models

We identify a duality transformation in one-dimensional hopping models that relates propagators in general disordered potentials linked by an up-down inversion of the energy landscape. This significantly generalises previous results for a duality between trap and barrier models. We use the resulting insights into the symmetries of these models to develop a real-space renormalisation scheme that can be implemented computationally and allows rather accurate prediction of propagation in these models. We also discuss the relation of this renormalisation scheme to earlier analytical treatments.