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

TL;DR

This paper maps mesoscopic resonant tunneling and multichannel Kondo problems to a quantum Brownian motion model, revealing phase diagrams, fixed points, and conductance resonance predictions using conformal field theory.

Contribution

It introduces a novel mapping of complex tunneling and Kondo problems to a quantum Brownian motion framework, enabling exact calculations of fixed points and conductance features.

Findings

Identification of localized, free, and intermediate phases depending on lattice symmetry.

Exact calculation of the fixed-point mobility using conformal field theory.

Prediction that the maximum conductance resonance is e^2/2h.

Abstract

We study mesoscopic resonant tunneling as well as multichannel Kondo problems by mapping them to a first-quantized quantum mechanical model of a particle moving in a multi-dimensional periodic potential with Ohmic dissipation. From a renormalization group analysis, we obtain phase diagrams of the quantum Brownian motion model with various lattice symmetries. For a symmorphic lattice, there are two phases at T=0: a localized phase in which the particle is trapped in a potential minimum, and a free phase in which the particle is unaffected by the periodic potential. For a non-symmorphic lattice, however, there may be an additional intermediate phase in which the particle is neither localized nor completely free. The fixed point governing the intermediate phase is shown to be identical to the well-known multichannel Kondo fixed point in the Toulouse limit as well as the resonance fixed point of a quantum dot model and a double-barrier Luttinger liquid model. The mapping allows us to compute the fixed-poing mobility $\mu^*$ of the quantum Brownian motion model exactly, using known conformal-field-theory results of the Kondo problem. From the mobility, we find that the peak value of the conductance resonance of a spin-1/2 quantum dot problem is given by $e^2/2h$. The scaling form of the resonance line shape is predicted.