活化扩散系统生存概率跨极限环的振荡衰减
Oscillatory decay of the survival probability of activated diffusion across a limit cycle
摘要：
布朗粒子在极限环上从稳定焦点的吸引域的激活逃逸表现出非克拉默斯行为：它是非泊松的。当吸引子移近边界时，生存概率会出现振荡。我们表明，这些振荡是由于复杂的值的高阶本征值的福克-普朗克算子，我们明确计算的小噪声的限制。我们还表明，在这个极限的振荡周期是激活的随机过程的缠绕数。这些峰值概率振荡与随机共振无关，并且在具有这里描述的拓扑结构的平面动力系统中应该是可检测的。
英文摘要：
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.
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