Detection of interactions via generalized factorial cumulants in systems in and out of equilibrium

TL;DR

This paper introduces generalized factorial cumulants of full counting statistics as a sensitive method to detect interactions in nanostructures, demonstrating their effectiveness in various regimes including equilibrium and non-equilibrium.

Contribution

The authors propose a new time-dependent cumulant-based approach that improves interaction detection over traditional methods, applicable to quantum dots in different regimes.

Findings

Generalized factorial cumulants detect interactions more effectively than ordinary cumulants.

Violation of a specific sign criterion indicates the presence of interactions.

Method works in both equilibrium and non-equilibrium conditions.

Abstract

We introduce time-dependent, generalized factorial cumulants $C_s^m(t)$ of the full counting statistics of electron transfer as a tool to detect interactions in nanostructures. The violation of the sign criterion $(-1)^{m-1} C^m_s(t)\ge0$ for \emph{any} time $t$, order $m$, and parameter $s$ proves the presence of interactions. For given system parameters, there is a minimal time span $t_\text{min}$ and a minimal order $m$ to observe the violation of the sign criterion. We demonstrate that generalized factorial cumulants are more sensitive to interactions than ordinary ones and can detect interactions even in regimes where ordinary factorial cumulants fail. We illustrate our findings with the example of a quantum dot tunnel coupled to electronic reservoirs either in or out of equilibrium.