7 A ug 2 00 3 Scattering Theory of Noise : Current and Charge Fluctuations in an ideal Conductor

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 /, set by the voltage. We also discuss fluctuations of charge in an ideal conductor. The manuscript is a revised and corrected version of JETP Lett.,70, 208 (1999). The discussion about charge fluctuations is restored (dropped from the JETPL text due to limitation in space). In an ideal conductor with electron transmission equal to unity (T = 1) the low-frequency shot noise is suppressed. This has been shown theoretically, using quantum-mechanical description in terms of the scattering matrix, for a quantum point contact [1–4], and even earlier, using kinetic equation for Fermions [5] and semi-classical Green's functions description [6], for ballistic point contacts. It has been also confirmed experimentally [7,8] for quantum point contacts. The same phenomenon has been predicted theoretically [9] and confirmed experimentally [10,11] for conductors in the fractional quantum Hall effect regime.