反应系统中稀有事件统计的WKB型近似
WKB-type-of approximation for rare event statistics in reacting systems
摘要：
我们计算的概率找到系统的反应粒子的状态，在很大程度上偏离典型的行为。从描述粒子数概率分布动力学的主方程得到稀有事件统计。我们通过母函数将主方程转化为含时的“薛定谔方程“。它的解决方案是提供了一个分离的anasterian和近似的静态部分，这是Wentzel-Kramers-Brillouin（WKB）型采用一个小参数。“经典”运动方程的解和鞍点近似产生适当的生成函数。我们的方法扩展了[V. Elgart和A. Kamenev，Phys.Rev.E70，041106（2004）]。我们计算罕见的事件统计系统的动态不能完全分析的分析方式。我们考虑不同的例子。
英文摘要：
We calculate the probabilities to find systems of reacting particles in states which largely deviate from typical behavior. The rare event statistics is obtained from the master equation which describes the dynamics of the probability distribution of the particle number. We transform the master equation by means of a generating function into a time-dependent "Schrödinger equation". Its solution is provided by a separation ansatz and an approximation for the stationary part which is of Wentzel-Kramers-Brillouin (WKB) type employing a small parameter. The solutions of the "classical" equations of motions and a saddle point approximation yield the proper generating function. Our approach extends a method put forward in [V. Elgart and A. Kamenev, Phys. Rev. E 70, 041106 (2004)]. We calculate the rare event statistics for systems where the dynamics cannot be entirely analyzed in an analytical manner. We consider different examples.
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