# Quantifying Non-Gaussian Diffusion in Transient Microscopy Using Excess Kurtosis

## TL;DR

This paper shows that non-Gaussian diffusion can be detected in transient microscopy by measuring excess kurtosis, improving analysis of charge carrier dynamics.

## Contribution

The study introduces excess kurtosis as a diagnostic tool for non-Gaussian diffusion in transient scattering microscopy data.

## Key findings

- Exciton populations in TMDCs show non-Gaussian profiles detectable via excess kurtosis.
- Anomalous diffusion simulations match experimental kurtosis signatures in coexisting populations.
- Discrete variable calculations provide robust diffusivity values where Gaussian fits fail.

## Abstract

Recent advances in transient microscopy have enabled
high-resolution
imaging of charge carrier dynamics. However, reliance on Gaussian
fits to quantify population broadening can lead to misinterpretation
when multiple species coexist. Transient scattering microscopy (TScM)
provides a powerful alternative, yet its sensitivity to diverse species
accentuates the limitations of traditional Gaussian fits. Here, we
use TScM to visualize exciton transport in bulk transition metal dichalcogenides
(TMDCs) and reveal that exciton populations exhibit non-Gaussian profiles
by analyzing their excess kurtosis. Simulations incorporating anomalous
diffusion reproduce these experimental observations and find that
the signature of the kurtosis is distinct for coexisting populations
and trap-dominated regimes. Additionally, we implement a discrete
variable calculation to extract the variances which yields robust,
consistent diffusivity values where Gaussian fits fail to do so. Our
results establish kurtosis as a vital diagnostic parameter for identifying
anomalous diffusion and demonstrate the necessity of moving beyond
Gaussian approximations for analysis of TScM data.