Non-Markovian dynamics in the theory of full counting statistics

TL;DR

This paper investigates how finite-bandwidth detectors induce non-Markovian effects in electron tunneling through quantum dots, revealing significant differences in current noise behavior compared to Markovian models.

Contribution

It introduces a theoretical framework for non-Markovian dynamics in full counting statistics, highlighting the impact of detector bandwidth on measured current cumulants.

Findings

Non-Markovian effects significantly alter current cumulant behavior.

Finite detector bandwidth leads to noise suppression interpretations.

The cumulant generating function captures non-Markovian dynamics effectively.

Abstract

We consider the theoretical description of real-time counting of electrons tunneling through a Coulomb-blockade quantum dot using a detector with finite bandwidth. By tracing out the quantum dot we find that the dynamics of the detector effectively is non-Markovian. We calculate the cumulant generating function corresponding to the resulting non-Markovian rate equation and find that the measured current cumulants behave significantly differently compared to those of a Markovian transport process. Our findings provide a novel interpretation of noise suppression found in a number of systems.