# Richardson diffusion in neurons

## TL;DR

This paper models ion transport in neurons affected by synaptic noise, demonstrating that the wave packet spreading follows Richardson diffusion, with analytical estimates of mean squared displacement.

## Contribution

It introduces a comb model framework for neuron ion diffusion influenced by multiplicative noise, revealing Richardson diffusion behavior.

## Key findings

- Mean squared displacement analyzed analytically
- Wave packet spreading corresponds to Richardson diffusion
- Model relevant to ion transport in noisy neuronal environments

## Abstract

The dynamics of an initial wave packed affected by random noise is considered in the framework of a comb model. The model is relevant to a diffusion problem in neurons where the transport of ions can be accelerated by an external random field due to synapse fluctuations. In the present specific case, it acts as boundary conditions, which lead to a reaction transport equation with multiplicative noise. The temporal behavior of the mean squared displacement is estimated analytically, and it is shown that the spreading of the initial wave packet corresponds to Richardson diffusion.