Richardson diffusion in neurons

The dynamics of an initial wave packet 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.