存在非热噪声时逃逸动力学的特殊性
Peculiarities of escape kinetics in the presence of athermal noises
摘要：
各种动态系统和反应网络的随机演化通常用噪声辅助的过阻尼粒子从势阱中逃逸来描述，如由范式朗之万方程设计的，其中加性高斯随机力再现了来自储层的热波动的影响。当系统接近平衡时，该方法正确地解释了由朗之万方程产生的轨迹的集合的玻尔兹曼分布的出现，并将噪声强度的强度与流动性联系起来。这种情况可以进一步推广到包括非高斯的影响，突发式强迫模型的Lévy噪声。然而，在这种情况下，脉动加性噪声不能被视为内部（热），因为摩擦强度和噪声方差之间的关系被破坏。Lévy噪声分布的重尾不仅有利于逃逸动力学，更重要的是，通过将最终定态改变为非玻尔兹曼非平衡形式来改变逃逸协议。因此，与高斯白噪声引起的动力学相反，在具有Lévy噪声的环境中，逃逸率不是由势垒高度决定的，而是由势垒宽度决定的。我们进一步讨论了热噪声和Lévy噪声的同时作用对双势阱中反应物通过时间和粒子数统计的影响。
英文摘要：
Stochastic evolution of various dynamic systems and reaction networks is commonly described in terms of noise assisted escape of an overdamped particle from a potential well, as devised by the paradigmatic Langevin equation in which additive Gaussian stochastic force reproduces effects of thermal fluctuations from the reservoir. When implemented for systems close to equilibrium, the approach correctly explains emergence of Boltzmann distribution for the ensemble of trajectories generated by Langevin equation and relates intensity of the noise strength to the mobility. This scenario can be further generalized to include effects of non-Gaussian, burst-like forcing modeled by Lévy noise. In this case however, the pulsatile additive noise cannot be treated as the internal (thermal), since the relation between the strength of the friction and variance of the noise is violated. Heavy tails of Lévy noise distributions not only facilitate escape kinetics, but more importantly, change the escape protocol by altering final stationary state to a non-Boltzmann, non-equilibrium form. As a result, contrary to the kinetics induced by a Gaussian white noise, escape rates in environments with Lévy noise are determined not by the barrier height, but instead, by the barrier width. We further discuss consequences of simultaneous action of thermal and Lévy noises on statistics of passage times and population of reactants in double-well potentials.
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