MATHEMATICAL ASPECTS OF THE FLUCTUATING BARRIER PROBLEM - EXISTENCE OF EQUILIBRIUM AND RELAXATION SOLUTIONS

For the simplest fluctuating barrier rate problem - diffusion in a sym metric double well over a barrier fluctuating randomly between 'high' and 'low' - we prove the existence of equilibrium and relaxation eigen vectors of the corresponding matrix of Smoluchowski diffusion operator s, thereby establishing the validity of rate calculations for this pro blem by the eigenvector-eigenvalue method. (C) 1998 Elsevier Science B .V. All rights reserved.