  Thermal decay rate over an edge-shaped barrier at high dissipation is studied
numerically through the computer modeling. Two sorts of the stochastic Langevin
type equations are applied: (i) the Langevin equations for the coordinate and
conjugate momentum (LEqp, the phase space diffusion) and (ii) the reduced
Langevin equation (RLE, the spatial diffusion, overdamped motion). The latter
method is much faster and self-similar; however, one can doubt about its
applicability in the case of an edge-shaped barrier with a discontinuous force.
The reason is that a formal condition of the applicability of the RLE is not
fulfilled since the curvature of the potential profile at the barrier is equal
to infinity. The present numerical study demonstrates that, for large friction,
the decay rate calculated using the RLE agrees with the rate resulting from the
more exact LEqp. Moreover, it turns out that the influence of the position of
the absorbing border is similar to the case of harmonic potential known in the
literature.
