Spectral theory of metastability and extinction in a branching-annihilation reaction

Abstract

We apply the spectral method, recently developed by the authors, to calculate the statistics of a reaction-limited multi-step birth-death process, or chemical reaction, that includes as elementary steps branching A->2A and annihilation 2A->0. The spectral method employs the generating function technique in conjunction with the Sturm-Liouville theory of linear differential operators. We focus on the limit when the branching rate is much higher than the annihilation rate, and obtain accurate analytical results for the complete probability distribution (including large deviations) of the metastable long-lived state, and for the extinction time statistics. The analytical results are in very good agreement with numerical calculations. Furthermore, we use this example to settle the issue of the "lacking" boundary condition in the spectral formulation.

8 pages, 4 eps figures, final version

References in corpus (4)

• Rare Events Statistics in Reaction--Diffusion Systems
• Spectral theory of metastability and extinction in birth-death systems
• Spectral formulation and WKB approximation for rare-event statistics in reaction systems
• Stochastic resonance due to internal noise in reaction kinetics

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