2004/01/12 by M. Moreau, Gleb Oshanin, G. Oshanin +4 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.69.046101
12 pages, appearing in PRE
arxiv created 2004/01/12 · openalex publication_date 2004/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a stochastic lattice theory describing the kinetic behavior of trapping reactions A+B-->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 the case when A stays immobile, than in situations when it moves.