Charge transfer counting statistics revisited

TL;DR

This paper revisits the quantum charge transfer statistics, deriving a new formula that accounts for charge coherence effects and differs from previous results, with implications for understanding quantum transport phenomena.

Contribution

The authors develop a revised counting statistics formula using gauge transformations, highlighting the role of charge coherence and correcting earlier approaches.

Findings

New formula differs from Levitov's when initial states are superpositions

Charge coherence significantly affects transfer statistics

Illustrated with single particle and tunnel junction examples

Abstract

Charge transfer statistics of quantum particles is obtained by analysing the time evolution of the many-body wave function. Exploiting properly chosen gauge transformations, we construct the probabilities for transfers of a discrete number of particles. Generally, the derived formula for counting statistics differs from the one previously obtained by Levitov {\it et al.} (J. of Math. Phys. {\bf 37}, 4845 (1996)). The two formulae agree only if the initial state is prohibited from being a superposition of different charge states. Their difference is illustrated for cases of a single particle and a tunnel junction, and the role of charge coherence is demonstrated.