Fickian Yet non-Gaussian Diffusion in Complex Molecular Fluids via a non-local diffusion framework

Fickian yet non-Gaussian diffusion (FnGD) has gained popularity in the recent times owing to it's ubiquity in a variety of complex fluids. However, whether FnGD can be observed experimentally in molecular fuids is still obscure with very little study in real systems. In this letter, we show existence of FnGD in molecular fluids based on compelling evidence from incoherent quasielastic neutron scattering (IQENS). Using a cage-jump diffsion model, we show that while the approach to Fickianity is exponentially fast, the Gaussianity is restored at a much slower algebraic rate. We propose a non-local diffusion (NLD) model to describe a d-dimensional jump-diffusion in FnGD regime and show their universal applicability in such systems. This study establishes that cage-jump diffusion process inevitably lead to FnGD and provides the framework of NLD models to explore such diffusion phenomena in any arbitrary dimensions.