Resonant tunneling and the multichannel Kondo problem: Quantum Brownian motion description

We study mesoscopic resonant tunneling and the multichannel Kondo problem by mapping them to a first-quantized quantum mechanical model of a particle moving in a multidimensional periodic potential and a dissipative medium. From renormalization group analyses, we obtain zero-temperature phase diagrams of the quantum Brownian motion models with various different lattice symmetries. Either stable, unstable, or both intermediate fixed points may be present depending on the symmetry. We also explicitly derive the direct mapping between the multilead quantum dot model and the multichannel Kondo model. Governed by the multichannel Kondo fixed point at low temperatures, the conductance between the leads follows a universal scaling function. We also calculate the on-resonance conductance and the scaling exponents are predicted.