Finite-velocity diffusion in the presence of a force

Abstract

We have studied a Cattaneo-Fick diffusion process in the presence of a deterministic force. Specifically, analytic results for the stationary probability distribution are solved for stable and unstable potentials. It is shown that the finite support as well as the shape of the stationary density are controlled by the telegrapher's parameters (relaxation time T and velocity of propagation θ). We have found the occurrence of a multimodality transition depending on the critical exponent of the potential and parameters T, θ. This research is motivated by the study of exact results for generic Smoluchoswki-like processes with finite-velocity diffusion.