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Effects of an oscillating field on a diffusion process in the presence of a trap
Authors:Moshe Gitterman  Shlomo Havlin  George H Weiss
Institution:(1) National Institutes of Health, 20892 Bethesda, Maryland;(2) Present address: Department of Physics, Bar-Ilan University, 52100 Ramat-Gan, Israel
Abstract:Consider a diffusion process on an infinite line terminated by a trap and modulated by a periodic field. When the frequency is equal to zero the mean time to trapping will be finite or infinite, depending on the sign of the field. We ask whether this behavior can be changed by an oscillatory field, and show that it cannot for pure Brownian motion. We suggest that transition can appear when the signal propagation velocity is finite as for the telegrapher's equation. We further suggest that the asymptotic time dependence of the survival probability is proportional tot –1/2 just as in the case of ordinary diffusion. The same conclusion is shown to hold for a system whose dynamics is governed by the equation 
$$\dot x = xv(t)/^\cdot L$$
, whereL is a constant.
Keywords:Brownian motion  stochastic resonance  trapping processes
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