FRICTIONAL TRAJECTORIES NEAR A BARRIER - A DISSIPATIONLESS NEWTONIAN APPROACH

We address the problem of classical frictional motion under a potentia l V possessing a barrier, apart from other possible confining and nons tationary terms. It is pointed out that the Green's solution of the ex act equation of motion can be reduced (under suitable conditions) eith er to an improved Rayleigh form or a non-Rayleigh form, the latter bei ng outside the scope of the standard large-friction treatment of the F okker-Planck equation. The resulting dissipationless dynamics involves an appropriately scaled potential which may have promising applicatio ns to quantum stochastic phenomena. Genuine dissipative corrections in regions far away from the barrier can be accounted for by the higher- order terms in our asymptotic expansions.