Full counting statistics in electric circuits

TL;DR

This paper reviews methods for defining and analyzing charge transfer statistics in electric circuits, exploring negative probabilities, detector effects, and phase coherence within a unified theoretical framework.

Contribution

It introduces a comprehensive review of counting statistics approaches, including the origin of negative probabilities and the impact of detectors and environment on charge transfer.

Findings

Negative probabilities arise in charge counting statistics.

Detector back action influences charge transfer statistics.

Phase coherence affects charge transfer in electromagnetic environments.

Abstract

We review several ways of defining the statistics of charge that is transmitted through an electric circuit, the so-called "counting statistics". We first pursue two approaches that explain the origin of "negative probabilities" that have been found earlier in this context. The first analysis involves degrees of freedom of the electric circuit only. In the second approach an idealized charge detector is introduced. We study then general linear detectors and how their back action on the electric conductor affects the statistics of transferred charge. Phase-coherent conductors in the presence of an electromagnetic environment are studied within a Keldysh action approach.