Mathematical aspects of the fluctuating barrier problem.: Existence of equilibrium and relaxation solutions Original Research Article

For the simplest fluctuating barrier rate problem – diffusion in a symmetric double well over a barrier fluctuating randomly between `highʹ and `lowʹ – we prove the existence of equilibrium and relaxation eigenvectors of the corresponding matrix of Smoluchowski diffusion operators, thereby establishing the validity of rate calculations for this problem by the eigenvector–eigenvalue method.