  In the last years, a few experiments in the fields of biological and soft
matter physics in colloidal suspensions have reported normal diffusion with a
Laplacian probability distribution in the particles displacements (i.e.,
Brownian yet non Gaussian diffusion). To model this behavior different
stochastic models had been proposed, with all of them introducing new random
elements that incorporate our lack of information about the media. Although
these models work in practice, due to their own nature a thorough understanding
of how the media interacts with itself and with the Brownian particle in
Brownian yet non Gaussian diffusion is outside of their aim and scope. For this
reason, a comprehensive mathematical model to explain Brownian yet non Gaussian
diffusion that includes molecular interactions is proposed in this paper. Based
on the theory of interfaces by Gennes and Langevin dynamics, it is shown that
long-range interactions in a weakly interacting fluid and in a microscopic
regime of zero viscosity leads to a Laplacian probability distribution in the
particles displacements. Further, it is shown that a phase transition can
explain a high diffusivity and causes this Laplacian distribution to evolve
towards a Gaussian via a transition probability in the interval of time as it
was observed in experiments. To validate these model predictions, the
experimental data of the Brownian motion of colloidal beads on phospholipid
bilayer by Wang et al. is used and compared with the results of the theory.
This comparison suggests that the proposed model not only is able to explain
qualitatively the Brownian yet non-Gaussian diffusion, but also quantitatively.
