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Lattice theory of trapping reactions with mobile species

M. Moreau·G. Oshanin·O. Benichou·M. Coppey
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Abstract

We present a stochastic lattice theory describing the kinetic behavior of trapping reactions $A + B \to B$, in which both the $A$ and $B$ particles perform an independent stochastic motion on a regular hypercubic lattice. Upon an encounter of an $A$ particle with any of the $B$ particles, $A$ is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables - "gates", imposed on each $B$ particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the $A$ particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time $t$, the $A$ particle survival probability is always larger in case when $A$ stays immobile, than in situations when it moves.

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M. Moreau, G. Oshanin, O. Benichou, M. Coppey. 2004-01-12. Lattice theory of trapping reactions with mobile species. https://doi.org/10.1103/physreve.69.046101

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