Escape over a potential barrier: The activation rate in bistable systems

The classical noise activated equilibration process for a particle moving in a metastable potential well is considered as an eigenproblem. The smallest nonzero real eigenvalue of Kramers' Fokker-Planck model is evaluated analytically by means of Rayleigh's quotient. The treatment allows both for asymmetry in the bistable potential and for arbitrary frictional dissipation. For weak damping the reaction rate tends to zero and depends on both initial and final states.