Rings and Boxes in Dissipative Environments

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 find, through a 2-loop renormalization group analysis, that a large dissipation parameter $\ensuremath{\eta}$ flows to a fixed point ${\ensuremath{\eta}}_{R}={\ensuremath{\eta}}_{c}=\ensuremath{\hbar}/2\ensuremath{\pi}$. 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 $\ensuremath{\eta}$. For finite $\ensuremath{\eta}>{\ensuremath{\eta}}_{c}$ we find that a certain average of the relaxation resistance is quantized. We propose a box experiment to measure a quantized noise.