# Non-Perturbative Electron Counting Statistics

## TL;DR

This paper introduces a non-perturbative method using hierarchical equations of motion to accurately analyze electron transport statistics in nanoscale systems, especially where traditional perturbative methods fail.

## Contribution

It develops a novel non-perturbative framework for full counting statistics applicable to systems with strong system-bath couplings, improving accuracy over perturbative approaches.

## Key findings

- Perturbative methods are inadequate for certain electron transfer regimes.
- The new framework accurately captures current fluctuations in complex systems.
- Comparison shows significant differences from traditional approaches.

## Abstract

The theory of full counting statistics allows complete characterization of charge transport processes through nanoscale systems. The majority of existing theoretical treatments used to obtain the current cumulants rely on perturbative approximations with respect to either the system-bath coupling or the electronic tunnelling coupling within the system. This is not generally well suited to electron transfer through organic molecules where these couplings can be on the same order of magnitude. Here we present a non-perturbative approach that uses the formalism of the hierarchical equations of motion to describe the system-bath dynamics while retaining a weak coupling with respect to source and drain leads. The scope of this new framework is demonstrated by comparisons with a perturbative approach for a dimer system coupled to a thermal bath. The inadequacy of the perturbative approach to describe current fluctuations in a variety of regimes is shown.