Statistics of charge transport and unconventional time ordering

TL;DR

This paper investigates charge transport statistics across a tunnel junction with energy-dependent scattering, revealing that unconventional time ordering affects current correlators but binomial statistics remain consistent.

Contribution

It introduces a model with quadratic dispersion and explores how different measurement protocols influence charge transport statistics, highlighting unconventional time ordering effects.

Findings

Unconventional time ordering alters current correlator expressions.

Binomial statistics are confirmed across various measurement protocols.

The model applies to both quadratic and linear dispersion relations.

Abstract

The statistics of charge transport across a tunnel junction with energy-dependent scattering is investigated. A model with quadratic dispersion relation is discussed in general and, independently, in the two limiting cases of a large detector and of a linear dispersion relation. The measurement of charge takes place according to various protocols. It is found that, as a rule, the statistics is expressed by means of time-ordered current correlators, differing however from the conventional ones in the ordering prescription. Nevertheless binomial statistics is confirmed in all cases.