非平衡系统中随机过程的最长游程
The longest excursion of stochastic processes in nonequilibrium systems
摘要：
我们考虑各种非平衡系统中随机过程的漂移，即连续零点之间的间隔，并研究最长的一个l_{\max}（t）到时间t的时间增长。对于光滑过程，我们发现了一个普适的线性增长< l_{\max}（t）> \simeq Q_{\infty} t，其振幅Q_ \infty依赖于模型.相反，对于具有持续性指数θ的非光滑过程，当θ<θ c时，< l_{\max}（t）>具有线性增长，而当θ> θ c时，< l_{\max}（t）> \sim t^{1-n}.振幅Q_{\infty}和指数ψ是与非平衡动力学相关的新量。这些行为是通过对更新和倍增过程的精确解析计算以及对其他系统如伊辛模型中的粗化动力学以及随机初始条件下的扩散方程的数值模拟得到的。
英文摘要：
We consider the excursions, i.e. the intervals between consecutive zeros, of stochastic processes that arise in a variety of nonequilibrium systems and study the temporal growth of the longest one l_{\max}(t) up to time t. For smooth processes, we find a universal linear growth < l_{\max}(t) > \simeq Q_{\infty} t with a model dependent amplitude Q_\infty. In contrast, for non-smooth processes with a persistence exponent θ, we show that < l_{\max}(t) > has a linear growth if θ< θ_c while < l_{\max}(t) > \sim t^{1-ψ} if θ> θ_c. The amplitude Q_{\infty} and the exponent ψare novel quantities associated to nonequilibrium dynamics. These behaviors are obtained by exact analytical calculations for renewal and multiplicative processes and numerical simulations for other systems such as the coarsening dynamics in Ising model as well as the diffusion equation with random initial conditions.
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