Narrow-escape-time problem: the imperfect trapping case

FÉLIX ROJO; H S WIO; CARLOS E. BUDDE

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2012 vol. 86 p. 1 - 10

1539-3755

We present a master equation approach to the emph{narrow escape time}(NET) problem, i.e. the time needed for a particle contained ina confining domain with a single narrow opening, to exitthe domain for the first time. We introduce a finite transitionprobability, $ u$, at the narrow escape window allowing the studyof the imperfect trapping case. Ranging from $0$ to $infty$, $ u$ allowed the study of both extremes of the trapping process: that of a highly deficient capture, and situations where escape is certain (``perfect trapping´´ case).We have obtained analytic results for the basic quantitystudied in the NET problem, the emph{mean escape time} (MET), and we havestudied its dependence in terms of the transition (desorption) probabilityover (from) the surface boundary, the confining domain dimensions, and thefinite transition probability at the escape window. Particularly we showthat the existence of a global minimum in the NET depends on the`imperfection´ of the trapping process. In addition to our analyticalapproach, we have implemented Monte Carlo simulations, finding excellentagreement between the theoretical results and simulations.%