Abstract
A new perturbation method of finding the stationary distribution function of the formP=Rexp(-φ/D) for a metastable (anharmonic) system driven by exponentially correlated noise is presented. The noise term is modeled by a Langevin equation and the stationary solution of the resultant (2+1)-dimensional Fokker-Planck equation is sought as a series expansion in the anharmonicity parameter around the known harmonic solution valid near the metastable minimum. The series converges for small τ in the leading order of the noise intensityD anywhere within the well. Analytic expressions forφ andR were found for a metastable and a bistable potential. The resultant decay rate is in accordance with previously published results. The method is suitable also for numerical calculations.
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Klik, I. Metastable systems driven by colored noise: The stationary state. J Stat Phys 63, 389–397 (1991). https://doi.org/10.1007/BF01026611
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DOI: https://doi.org/10.1007/BF01026611