Brownian diffusion in non-harmonic potentials

Brownian motion in confined systems is widespread in soft matter physics, biophysics, statistical physics and related fields. In most of these systems, a Brownian particle cannot freely diffuse in the space but is confined by a potential well in a limited range of positions. When performing data analysis, typically the harmonic assumption is made, assuming that in the regions explored by the particle during its dynamics, the confining potential is fairly well described by a harmonic potential. This is however not valid a priori. In this work, it is shown how the diffusion coefficient and the potential width obtained through standard analysis underlying a harmonic approximation are affected by increasing errors when moving away from the conditions under which harmonic approximation is legitimate. These observations motivate the research of a more general method for properly obtaining the diffusion coefficient for a particle diffusing in a generic potential well. Here, a method is proposed that allows retrieving the correct diffusion coefficient by comparing the original data and ad hoc simulations without any a priori knowledge of the potential.