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We examine dissipation effects in a multichannel quantum RC circuit,comprising a cavity or single-electron box capacitively coupled to a gate andconnected to a reservoir lead via several conducting channels. Depending on theengineering details of the quantum RC circuit, the number of channelscontributing to transport vary, as do the form of the interchannel couplings.For low-frequency AC transport, the charge-relaxation resistance ($R_{q}$) is anontrivial function of the parameters of the system. However, in the vicinityof the charge degeneracy points and for weak tunneling, we find as a result ofcross-mode mixing or channel asymmetry that $R_q$ becomes universal for ametallic cavity at low temperatures, and equals the unit of quantum resistance.To prove this universality we map the system to an effective one-channel Kondomodel, and construct an analogy with the Coulomb gas. Next, we probe theopposite regime of near-perfect transmission using a bosonization approach.Focussing on the two-channel case, we study the effect of backscattering at thelead-dot interface, more specifically, the role of an asymmetry in thebackscattering amplitudes, and make a connection with the weak tunneling regimenear the charge degeneracy points.

Strongly correlated dynamics in multichannel quantum RC circuits