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

Michael Assaf·Baruch Meerson
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Abstract

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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Michael Assaf, Baruch Meerson. 2006-09-23. Spectral formulation and WKB approximation for rare-event statistics in reaction systems. https://doi.org/10.1103/physreve.74.041115

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