Saddle point avoidance due to inhomogeneous friction

The saddle point avoidance due to a position dependent friction is examined in a bidimensional model which can be solved numerically. Both the analysis of the kinetic flux and the covariant representation of the Fokker-Planck equation lead to a scalar potential which has the same form of the effective potential derived by Berkowitz et al. [J. Chem. Phys, 79 (1983) 5563] by employing the 'minimum resistance path' method. The saddle point avoidance is then explained by the contribution of the friction inhomogeneity, which displaces the effective saddle point with respect to that of the bare potential. In order to derive the transition rate, however, also the gradient of the kinetic eigenfunction along the stochastic separatrix should be evaluated, A variational procedure based on the Rayleigh quotient has been employed to this purpose, with a fair agreement in the comparison with the exact numerical results.