Spectral formulation and WKB approximation for rare-event statistics in reaction systems

Details Spectral formulation and WKB approximation for rare-event statistics in reaction systems Spectral formulation and WKB approximation for rare-event statistics in reaction systems

2006-06-08

arxiv.org/abs/cond-mat/0606210v2

Physics

Condensed Matter

Statistical Mechanics

11 pages, 10 eps figures

Scientific paper

10.1103/PhysRevE.74.041115

We develop a spectral formulation and a stationary WKB approximation for calculating the probabilities of rare events (large deviations from the mean) in systems of reacting particles with infinite-range interaction, describable by a master equation. We compare the stationary WKB approximation with a recent time-dependent semiclassical approximation developed, for the same class of problems, by Elgart and Kamenev. As a benchmark we use an exactly solvable problem of the binary annihilation reaction 2A -> 0.

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