Oscillatory decay of the survival probability of activated diffusion across a limit cycle

Autor:	Duc, K. Dao, Schuss, Z., Holcman, D.
Rok vydání:	2013
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs Mathematics - Probability Physics - Classical Physics 35P20 82-08 60G07 60-08 G.3 G.1.8
Druh dokumentu:	Working Paper
Popis:	Activated escape of a Brownian particle from the domain of attraction of a stable focus over a limit cycle exhibits non-Kramers behavior: it is non-Poissonian. When the attractor is moved closer to the boundary oscillations can be discerned in the survival probability. We show that these oscillations are due to complex-valued higher order eigenvalues of the Fokker-Planck operator, which we compute explicitly in the limit of small noise. We also show that in this limit the period of the oscillations is the winding number of the activated stochastic process. These peak probability oscillations are not related to stochastic resonance and should be detectable in planar dynamical systems with the topology described here. Comment: Oscillation peaks. Asymptotic computation of the spectrum for a non-selfadjoint second order operator
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1312.6992 Zobrazit plný text záznamu View this record from Arxiv