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

TL;DR

This paper develops a comprehensive scattering theory for current and charge noise in ideal quantum conductors, providing exact formulas for spectral density and revealing a finite shot noise with a singularity at a specific frequency.

Contribution

It introduces the most complete scattering theory for noise in noninteracting conductors, including exact spectral density formulas and analysis of charge fluctuations.

Findings

Finite shot noise at finite frequency in ideal conductors.

Spectral density exhibits a singularity at the Josephson frequency.

Provides exact formulas in terms of scattering matrix.

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 $\omega =eV/\hbar $, set by the voltage. We also discuss fluctuations of charge in an ideal conductor.