Frequency-dependent counting statistics in interacting nanoscale conductors

TL;DR

This paper introduces a formalism for calculating finite-frequency current correlations in interacting nanoscale conductors, revealing how higher-order cumulants depend on frequency and are crucial for understanding interactions.

Contribution

The authors develop a spectral decomposition-based method to compute finite-frequency cumulants in interacting systems, enabling analysis of complex fluctuation statistics.

Findings

Finite-frequency third cumulant varies significantly with frequency.

Deviations from Poissonian behavior depend strongly on frequency.

Higher-order cumulants are essential for characterizing interactions.

Abstract

We present a formalism to calculate finite-frequency current correlations in interacting nanoscale conductors. We work within the n-resolved density matrix approach and obtain a multi-time cumulant generating function that provides the fluctuation statistics, solely from the spectral decomposition of the Liouvillian. We apply the method to the frequency-dependent third cumulant of the current through a single resonant level and through a double quantum dot. Our results, which show that deviations from Poissonian behaviour strongly depend on frequency, demonstrate the importance of finite-frequency higher-order cumulants in fully characterizing interactions.