  We study the motion of a particle in a periodic potential with Ohmic
dissipation. In $D=1$ dimension it is well known that there are two phases
depending on the dissipation: a localized phase with zero temperature mobility
$\mu=0$ and a fully coherent phase with $\mu$ unaffected by the periodic
potential. For $D>1$, we find that this is also the case for a Bravais lattice.
However, for non symmorphic lattices, such as the honeycomb lattice and its $D$
dimensional generalization, there is a new intermediate phase with a universal
mobility $\mu^*$. We study this intermediate fixed point in perturbatively
accessible regimes. In addition, we relate this model to the Toulouse limit of
the $D+1$ channel Kondo problem. This mapping allows us to compute $\mu^*$
exactly using results known from conformal field theory. Experimental
implications are discussed for resonant tunneling in strongly coupled Coulomb
blockade structures and for multi channel Luttinger liquids.
