Measurement of high order current correlators

TL;DR

This paper analyzes the feasibility of measuring high-order current correlators using linear detectors, deriving exact expressions and exploring measurement scenarios for fluctuation spectra and unequal-time correlators.

Contribution

It provides formally exact expressions for high-order current correlators in terms of Keldysh time-ordered operators and clarifies the time ordering in measurements of unequal-time correlators.

Findings

Derived explicit time ordering for current correlators.

Analyzed measurement of correlators at different points in a conductor.

Provided formal expressions for detector outputs in high-order current measurements.

Abstract

The feasibility of measuring high-order current correlators by means of a linear detector is analyzed. Two different types of measurements are considered: measurement of fluctuation power spectrum and measurement of unequal-time current correlators at fixed points in time. In both cases, formally exact expressions in terms of Keldysh time-ordered electron current operators are derived for the detector output. An explicit time ordering is found for the current correlators under the expectation operator used in measurements of high order unequal-time current correlators. The situation when a detector measures current correlators at different points of a conductor is considered.