On the non-Markovian theory of activated rate processes in the small friction limit

The motion of a particle in a one-dimensional potential well under the effect of thermal noise and damping plays an important role in modeling many physical and chemical phenomena. The problem of interest is to determine the escape rate χ from the well. The generalized Langevin equation, describing this motion, is examined in the asymptotic limit of the small friction. A limiting backward Kolmogorov operator in the energy variable is derived by averaging on constant energy contours, and then employed to calculate explicit analytical expressions for the activation rate χ.