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

Abstract

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 ${\mu }^{\ast }$. 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 ${\mu }^{\ast }$ 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.

arXiv comment4 pages REVTeX, 3 postscript figures (uuencoded and compressed). A numerical error in the on resonance conductance of the Coulomb blockade structure has been corrected