Low-dimensional turnover theory of thermal activation

Kramers' Fokker-Planck model for activated rate processes (noise-induced escape over a potential-energy barrier) is solved without recourse to any microscopic theory (Grabert [Phys. Rev. Lett. 61, 1683 (1988)]) or associated Langevin equations (Graham [J. Stat. Phys. 60, 675 (1990)]). The independence of the microscopy of Grabert's original result for the escape rate is thereby definitely proven and clarified. Throughout, the analysis is systematic in a small parameter and provides a unified treatment of both weak and strong friction, including the turnover regime. Inter alia we introduce some novel theoretical concepts, such as a constrained Gaussian transformation and a dynamical extension of phase space. Finite-barrier corrections are also investigated.