Quantum versus classical counting in nonMarkovian master equations

TL;DR

This paper compares quantum and classical approaches to full counting statistics in non-Markovian quantum transport, highlighting how quantum effects influence current and shot noise spectra.

Contribution

It demonstrates the fundamental differences in noise spectra when charge is treated quantum mechanically versus classically in non-Markovian master equations.

Findings

Classical description yields frequency-independent noise spectra.

Quantum treatment reveals frequency-dependent noise effects.

Quantum effects are essential for accurate shotnoise characterization.

Abstract

We discuss the description of full counting statistics in quantum transport with a nonMarkovian master equation. We focus on differences arising from whether charge is considered as a classical or a quantum degree of freedom. These differences manifest themselves in the inhomogeneous term of the master equation which describes initial correlations. We describe the influence on current and in particular, the finite-frequency shotnoise. We illustrate these ideas by studying transport through a quantum dot and give results that include both sequential and cotunneling processes. Importantly, the noise spectra derived from the classical description are essentially frequency-independent and all quantum noise effects are absent. These effects are fully recovered when charge is considered as a quantum degree of freedom.