Quantum Brownian motion in a periodic potential and the multichannel 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. However, for nonsymmorphic lattices with D>1, such as the honeycomb lattice, there is an intermediate phase with a universal mobility mu*. This intermediate phase is relevant to resonant tunneling experiments in strongly coupled Coulomb-blockade structures as well as multichannel Luttinger liquids. We relate this problem to the Toulouse limit of the D + 1 channel Kondo problem, which allows us to compute mu* exactly using results known from conformal field theory.