Received 21 January 2011; published 19 April 2011
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 η flows to a fixed point ηR=ηc=ℏ/2π. 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 η. For finite η>ηc we find that a certain average of the relaxation resistance is quantized. We propose a box experiment to measure a quantized noise.