Mathematical aspects of the fluctuating barrier problem. Explicit equilibrium and relaxation solutions

The diffusive kinetics in a symmetric double well with a high barrier fluctuating randomly in time is investigated by means of the corresponding Fokker–Planck equation. In the Smoluchowski limit explicit solutions for the equilibrium and the relaxation eigenfunctions are given. Moreover, the least negative eigenvalue, the relaxation rate, is calculated for all values of the barrier fluctuation rate.