Multi-barrier crossing regulated by the friction

In the presence of saddle points having the same energy, multi-barrier transitions, which normally are quenched in the over-damped regime, become allowed when the friction is small enough. The model described by the Fokker-Planck equation for the angle and its velocity with a fourfold potential is examined in order to illustrate the role of the friction in the multi-barrier crossing. Both exact numerical calculations and asymptotic analysis of the Fokker-Planck equation are performed. Some general conclusions are drawn for the butane isomerization.