Universal resistances of the quantum resistance-capacitance circuit

Mesoscopic circuits cooled down to low temperatures witness marked non-local effects in their transport properties because of electron coherenceĝ€"electron wavefunctions spread over the sample and correlate its different parts. One of the consequences is that, in one dimension, the maximum d.c. conductance is quantized in steps of e ² /h. Here we extend the concept of e ² /huniversal quantized resistance'to the a.c. regime. We analyse the coherent quantum resistanc-capacitance circuit comprising a cavity capacitively coupled to a gate and connected by means of a single spin-polarized channel to a reservoir lead. We show that, as a result of the Coulomb interaction and global phase coherence, the charge relaxation resistance Rq is identical for weak and large transmissions and that it smoothly changes from h/2e ² to h/e ² when the frequency exceeds the level spacing of the cavity. For large cavities, we relate the resistance h/e ² to the Korring-Shiba relation of the Kondo model. Finally, we introduce a larger class of models with a universal charge relaxation resistance.