Frictional trajectories near a barrier: a dissipationless Newtonian approach

We address the problem of classical frictional motion under a potential V possessing a barrier, apart from other possible confining and nonstationary terms. It is pointed out that the Green's solution of the exact equation of motion can be reduced (under suitable conditions) either to an improved Rayleigh form or a non-Rayleigh form, the latter being outside the scope of the standard large-friction treatment of the Fokker-Planck equation. The resulting dissipationless dynamics involves an appropriately scaled potential which may have promising applications 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. (author)