Survival of interacting diffusing particles inside a domain with absorbing boundary

Tal Agranov, Baruch Meerson, Arkady Vilenkin

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15 Scopus citations


Suppose that a d-dimensional domain is filled with a gas of (in general, interacting) diffusive particles with density n0. A particle is absorbed whenever it reaches the domain boundary. Employing macroscopic fluctuation theory, we evaluate the probability P that no particles are absorbed during a long time T. We argue that the most likely gas density profile, conditional on this event, is stationary throughout most of the time T. As a result, P decays exponentially with T for a whole class of interacting diffusive gases in any dimension. For d=1 the stationary gas density profile and P can be found analytically. In higher dimensions we focus on the simple symmetric exclusion process (SSEP) and show that -lnP≃D0TLd-2s(n0), where D0 is the gas diffusivity, and L is the linear size of the system. We calculate the rescaled action s(n0) for d=1, for rectangular domains in d=2, and for spherical domains. Near close packing of the SSEP s(n0) can be found analytically for domains of any shape and in any dimension.

Original languageAmerican English
Article number012136
JournalPhysical Review E
Issue number1
StatePublished - 20 Jan 2016

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© 2016 American Physical Society.


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