Probability distribution to obtain the characteristic passage time for different tri-stable potentials

Abstract

The purpose of this work is to explore the kinetics of the transition probability distribution obtained as a solution to the Fokker–Planck equation (FPE) for a system described by a potential function (free energy) that has three regions of minimum, a tri-stable potential. The Fokker–Planck equation is rewritten as a Schrödinger equation (SE) and this allows the use of the Supersymmetric Quantum Mechanics formalism (SQM) associated to the variational method to obtain the analytical approximated spectrum. From the solutions obtained the probability distribution is evaluated which allows the determination of the characteristic passage time between the three potential minima. The results show the dependence between the diffusion process and the relative depth between of the central and the lateral minima of the potential.