Statistics of Charge Fluctuations in Chaotic Cavities

TL;DR

This paper derives a universal statistical description of charge fluctuations in chaotic mesoscopic cavities, applicable to various observables and conditions, using scattering matrix and random matrix theory.

Contribution

It introduces a semi-analytical method to evaluate charge fluctuation statistics in chaotic cavities, extending to arbitrary contact transparency and small capacitance regimes.

Findings

Universal charge fluctuation statistics derived

Fluctuations characterized for equilibrium and non-equilibrium

Suppression of fluctuations in small capacitance limit

Abstract

We consider the zero frequency fluctuations of charge inside a mesoscopic conductor in the large capacitance limit. In analogy to current counting statistics we derive the characteristic function of charge fluctuations in terms of the scattering matrix of the conductor. Using random matrix theory we evaluate the characteristic function semi-analytically for chaotic cavities. Our result is universal in the sense that it describes not only the fluctuations of charge, but of any observable quantity inside the cavity. We discuss equilibrium and non-equilibrium fluctuations and extend our theory to the case of contacts with arbitrary transparency. Finally we investigate the suppression of fluctuations in the small capacitance limit due to charge screening.