Time-dependent factorial cumulants in interacting nano-scale systems

TL;DR

This paper investigates how interactions in nano-scale systems cause the zeros of the generating function to become complex, leading to oscillatory behavior in high-order factorial cumulants over time, demonstrated through a quantum dot model.

Contribution

It reveals the impact of interactions on the zeros of the generating function and the resulting oscillations in factorial cumulants, extending understanding beyond non-interacting systems.

Findings

Zeros of the generating function become complex with interactions.

Factorial cumulants oscillate strongly over time when interactions are present.

Without interactions, factorial cumulants are monotonic functions of time.

Abstract

We discuss time-dependent factorial cumulants in interacting nano-scale systems. Recent theoretical work has shown that the full counting statistics of non-interacting electrons in a two-terminal conductor is always generalized binomial and the zeros of the generating function are consequently real and negative. However, as interactions are introduced in the transport, the zeros of the generating function may become complex. This has measurable consequences: With the zeros of the generating function moving away from the real-axis, the high-order factorial cumulants of the transport become oscillatory functions of time. Here we demonstrate this phenomenon on a model of charge transport through coherently coupled quantum dots attached to voltage-biased electrodes. Without interactions, the factorial cumulants are monotonic functions of the observation time. In contrast, as interactions are introduced, the factorial cumulants oscillate strongly as functions of time. We comment on possible measurements of oscillating factorial cumulants and outline several avenues for further investigations.