A pseudospectral solution of a Fokker-Planck equation to model isomerization reactions

Abstract

A Fokker-Planck equation is used to model a reactive system with two stable states. The barrier of the potential that separates the states is controlled with a parameter, ϵ, that alters the height of the barrier that separates the two states of the system. The rate of transitions between the two states, equivalently the rate of reaction, can be treated with a transition state theory as for a large class of chemical reactions. The Fokker-Planck equation is solved with a pseudospectral method based on nonclassical basis polynomials. The time dependent solution is expressed in terms of the eigenvalues and eigenfunctions of the linear Fokker-Planck operator. This eigenvalue problem can be written as the solution of a Schrödinger equation with a potential function defined by the drift and diffusion coefficients in the Fokker-Planck equation.