Inverse counting statistics based on generalized factorial cumulants

TL;DR

This paper introduces a method to infer key characteristics of unknown stochastic systems using generalized factorial cumulants derived from long-time full counting statistics, revealing hidden system features.

Contribution

It presents a novel inverse counting-statistics procedure utilizing generalized factorial cumulants to reconstruct system dimensions and relaxation rates from limited data.

Findings

Reconstructed lower bounds of system dimensions.

Determined full spectrum of relaxation rates.

Revealed hidden system features not accessible by ordinary cumulants.

Abstract

We propose a procedure to reconstruct characteristic features of an unknown stochastic system from the long-time full counting statistics of some of the system's transitions that are monitored by a detector. The full counting statistics is conveniently parametrized by so-called generalized factorial cumulants. Taking only a few of them as input information is sufficient to reconstruct important features such as the lower bound of the system dimension and the full spectrum of relaxation rates. The use of generalized factorial cumulants reveals system dimensions and rates that are hidden for ordinary cumulants. We illustrate the inverse counting-statistics procedure for two model systems: a single-level quantum dot in a Zeeman field and a single-electron box subjected to sequential and Andreev tunneling.