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Charge Relaxation Resistances and Charge Fluctuations in Mesoscopic Conductors

A brief overview is presented of recent work which investigates the time-dependent relaxation of charge and its spontaneous fluctuations on mesoscopic conductors in the proximity of gates. The leading terms of the low frequency conductance are determined by a capacitive or inductive emittance and a dissipative charge relaxation resistance. The charge relaxation resistance is determined by the ratio of the mean square dwell time of the carriers in the conductor and the square of the mean dwell time. The contribution of each scattering channel is proportional to half a resistance quantum. We discuss the charge relaxation resistance for mesoscopic capacitors, quantum point contacts, chaotic cavities, ballistic wires and for transport along edge channels in the quantized Hall regime. At equilibrium the charge relaxation resistance also determines via the fluctuation-dissipation theorem the spontaneous fluctuations of charge on the conductor. Of particular interest are the charge fluctuations in the presence of transport in a regime where the conductor exhibits shot noise. At low frequencies and voltages charge relaxation is determined by a nonequilibrium charge relaxation resistance.