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

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 to a recent time-dependent semiclassical approximation developed, for the same class of problems, by Elgart and Kamenev [Phys. Rev. E 70, 41106 (2004)]. As a benchmark we use an exactly solvable problem of the binary annihilation reaction $2A\to \stackrel{̸}{0}$.