Quantum and Classical Binomial Distributions for the Charge Transmitted through Coherent Conductor

TL;DR

This paper compares quantum and classical binomial distributions for charge transfer in coherent conductors, revealing their distinct limits, measurable high-order correlators, and oscillating frequency dependencies in current fluctuations.

Contribution

It clarifies the difference between quantum and classical binomial distributions in charge transport and explores their measurable high-order correlators and frequency-dependent oscillations.

Findings

Two universal limits: quantum and semiclassical distributions.

High-order current correlators exhibit oscillating frequency dependence.

Different setups yield substantially different contributions to oscillating terms.

Abstract

We discuss controversial results for the statistics of charge transport through coherent conductors. Two distribution functions for the charge transmitted was obtained previously, first by L.Levitov and G.Lesovik, [JETP Letters Vol.55 p.555 (1992)] and the other initially by the same authors [ibid. Vol.58 p.230 (1993)], and later the result was reproduced by several authors. The latter distribution functions actually coincides with classical binomial distribution (though obtained purely quantum mechanically) former (result of 1992) is different and we call it here quantum binomial distribution. The two distribution function represent two opposite universal limits - one is purely quantum, where interference is important, and the other is semiclassical, where interference is smeared out. We show, that high order charge correlators, determined by the either distribution functions, can all be measured in different setups. The high order current correlators, starting the third order, reveal (missed in previous studies) special oscillating frequency dependence on the scale of the inverted time flight from the obstacle to the measuring point. Depending on setup, the oscillating terms give substantially different contributions.