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

Michael Assaf*, Baruch Meerson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


We apply the spectral method, recently developed by the authors, to calculate the statistics of a reaction-limited multistep 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.

Original languageAmerican English
Article number031122
JournalPhysical Review E
Issue number3
StatePublished - 29 Mar 2007


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