Rings and Coulomb boxes in dissipative environments

TL;DR

This paper investigates a dissipative quantum system on a ring, revealing a fixed point in dissipation, quantized relaxation resistance, and proposing an experiment to measure quantized noise, linking non-equilibrium response to equilibrium properties.

Contribution

It demonstrates a fixed point in dissipation parameter flow, quantizes relaxation resistance in Coulomb box systems, and proposes an experimental measurement of quantized noise.

Findings

Large dissipation flows to a fixed point ta^R=5/224

Relaxation resistance is quantized at large ta

Proposes Coulomb box experiment to measure quantized noise

Abstract

We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a DC field. We show how this non-equilibrium response is related to a flux averaged equilibrium response. We find, through a 2-loop renormalization group analysis, that a large dissipation parameter \eta flows to a fixed point \eta^R=\hbar/2\pi. We also reexamine the mapping of this problem to that of the Coulomb box and show that the relaxation resistance, of recent interest, is quantized for large \eta. For finite \eta>\eta^R we find that a certain average of the relaxation resistance is quantized. We propose a Coulomb box experiment to measure a quantized noise.