Quantum Brownian Motion in a Periodic Potential and the Multi Channel Kondo Problem

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.