Rings and Coulomb boxes in dissipative environments

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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 ηflows to a fixed point ηʳ=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>ηʳ we find that a certain average of the relaxation resistance is quantized. We propose a Coulomb box experiment to measure a quantized noise.