Statistics of current fluctuations at non-zero frequencies

TL;DR

This paper develops a comprehensive method to analyze current fluctuation statistics in mesoscopic conductors at various frequencies, revealing significant dispersion effects and potential sign changes in the third cumulant at certain frequency ranges.

Contribution

It introduces a general approach for current fluctuation statistics applicable at arbitrary frequencies and interactions, and applies it to reveal new dispersion phenomena in the third cumulant.

Findings

Frequency dispersion of the third cumulant is significant at voltages.

Dispersion can cause the sign change of the third cumulant.

The approach applies to both interacting and non-interacting conductors.

Abstract

We formulate a general approach which describes statistics of current fluctuations in mesoscopic coherent conductors at arbitrary frequencies and in the presence of interactions. Applying this approach to the non-interacting case, we analyze frequency dispersion of the third cumulant of the current operator ${\cal S}_3$ at frequencies well below both the inverse charge relaxation time and the inverse electron dwell time. This dispersion turns out to be important in the frequency range comparable to applied voltages. For comparatively transparent conductors it may lead to the sign change of ${\cal S}_3$