Charge relaxation and dephasing in Coulomb-coupled conductors

The dephasing time in coupled mesoscopic conductors is caused by the fluctuations of the dipolar charge permitted by the long-range Coulomb interaction. We relate the phase breaking time to elementary transport coefficients that describe the dynamics of this dipole: the capacitance, an equilibrium charge relaxation resistance, and in the presence of transport through one of the conductors a nonequilibrium charge relaxation resistance. The discussion is illustrated for a quantum point contact in a high magnetic field in proximity to a quantum dot.