  We discuss the physical consequences of a duality between two models with
quenched disorder, in which particles propagate in one dimension among random
traps or across random barriers. We derive an exact relation between their
diffusion fronts at fixed disorder, and deduce from this that their
disorder-averaged diffusion fronts are exactly equal. We use effective dynamics
schemes to isolate the different physical processes by which particles
propagate in the models and discuss how the duality arises from a
correspondence between the rates for these different processes.
