Annealed versus quenched diffusion coefficient in random media

We examine two a priori different definitions of a diffusion coefficient for tracer particles in static random media. The ‘‘quenched’’ diffusion coefficient $D^Q$ characterizes the spread of a packet in a single environment. The ‘‘annealed’’ coefficient $D^A$ characterizes the spread of the configuration-averaged packet. For one-dimensional diffusion with a drift $D^A$>$D^Q$ whereas d>1$D^A$=$D^Q$. For some models displaying anomalous diffusion we also find $D^A$>$D^Q$. .AE