Full distribution of first exit times in the narrow escape problem

In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic pr...

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Bibliographic Details
Published in:New journal of physics 2019-12, Vol.21 (12), p.122001
Main Authors: Grebenkov, Denis S, Metzler, Ralf, Oshanin, Gleb
Format: Article
Language:English
Subjects:
Chemical Sciences
Containers
Defocusing
Entrances
first-passage time distribution
Mathematics
mean versus most probable reaction times
mixed boundary conditions
narrow escape problem
or physical chemistry
Parameters
Physics
Reaction time
Statistics
Theoretical and
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Summary:In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ab5de4