Time-dependent factorial cumulants in interacting nano-scale systems

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.