Charge fluctuations in quantum point contacts and chaotic cavities in the presence of transport

We analyze the frequency-dependent current fluctuations induced into a gate near a quantum point contact or a quantum chaotic cavity. We use a current- and charge-conserving effective scattering approach in which interactions are treated in the random-phase approximation. The current fluctuations measured at a nearby gate, coupled capacitively to the conductor, are determined by the screened charge fluctuations of the conductor. Both the equilibrium and nonequilibrium current noise at the gate can be expressed with the help of resistances which are related to the charge dynamics on the conductor. We evaluate these resistances for a point contact, and determine their distributions for an ensemble of chaotic cavities. For a quantum point contact these resistances exhibit pronounced oscillations with the opening of channels. For a chaotic cavity coupled to one-channel point contacts, the charge relaxation resistance shows a broad distribution between $\frac{1}{4}$ and $\frac{1}{2}$ of a resistance quantum. The nonequilibrium resistance exhibits a broad distribution between zero and $\frac{1}{4}$ of a resistance quantum.