Two Coupled Mechanisms Produce Fickian, yet non-Gaussian Diffusion in Heterogeneous Media

In several biological and soft matter systems, Fickian yet non-Gaussian diffusion has been observed, where the mean square displacement remains linear in nature, but the displacement distribution is non-Gaussian. The underlying reasons behind this strange behavior still remain speculative. Here, we perform a set of controlled experiments that quantitatively explore the effect of spatial heterogeneities on the appearance of non-Gaussianity in Fickian diffusion. Specifically, we study the diffusion of fluorescent colloidal particles in a matrix of lithographically fabricated micropillar arrays having a range of structural configurations: from completely ordered to completely random. Structural randomness and density are found to be the two most decisive factors in making diffusion non-Gaussian. We show that non-Gaussianity emerges as a direct consequence of two coupled physical mechanisms that produce a superstatistical behavior of the ensemble in a structurally heterogeneous environment. The two mechanisms identified here are relevant for many systems of crowded heterogeneous environments where non-Gaussian diffusion is frequently observed, for example in biological systems, polymers, gels and porous materials.