Kinetic regimes in coupled systems

The role of the diffusion anisotropy is analyzed for a system of two coupled coordinates x and y subjected to a bistable potential. Exact numerical results for the first few eigenmodes (rate constants) are compared with approximate results which are correct at extreme values of the anisotropy ratio D(x)/D(y), but at finite values of the energy barrier. This contribution is given for a better understanding of the validity of asymptotic formulas for the decay rate of a metastable population, which have been proposed, among the others, by the "Northwestern" group of Dygas and co-workers, and by the "Karpov" group of Berezhkovskii and Zitserman.