Scattering Theory of Noise: Current and Charge Fluctuations in an ideal Conductor

Abstract

We present the most complete scattering theory for noise in noninteracting case. The exact formula for spectral density of current fluctuations at finite frequency is presented in terms of scattering matrix for a coherent quantum conductor. We show that the shot noise at finite frequency in an ideally conducting contact is finite and the spectral density of the noise has a singularity at the "Josephson" frequency $ω=eV/\hbar $, set by the voltage. We also discuss fluctuations of charge in an ideal conductor.