Quantum Brownian motion in a periodic potential and the multichannel 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 $\ensuremath{\mu}=0$ and a fully coherent phase with $\ensuremath{\mu}$ unaffected by the periodic potential. However, for nonsymmorphic lattices with $Dg1$, such as the honeycomb lattice, there is an intermediate phase with a universal mobility ${\ensuremath{\mu}}^{*}$. 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 ${\ensuremath{\mu}}^{*}$ exactly using results known from conformal field theory.