Szabat Bozena, Weron Karina, Hetman Paulina
Institute of Physics, Wroclaw University of Technology, 50-370 Wroclaw, Poland.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Feb;75(2 Pt 1):021114. doi: 10.1103/PhysRevE.75.021114. Epub 2007 Feb 16.
The wait-and-switch stochastic model of relaxation is presented. Using the "random-variable" formalism of limit theorems of probability theory we explain the universality of the short- and long-time fractional-power laws in relaxation responses of complex systems. We show that the time evolution of the nonequilibrium state of a macroscopic system depends on two stochastic mechanisms: one, which determines the local statistical properties of the relaxing entities, and the other one, which determines the number (random or deterministic) of the microscopic and mesoscopic relaxation contributions. Within the proposed framework we derive the Havriliak-Negami and Kohlrausch-Williams-Watts functions. We also discuss the influence of the random-walk characteristics of migrating defects on the homogeneous and heterogeneous relaxation scenarios and show the origins of the stretched-exponential integral kernel in the integral representation of the ensemble-averaged relaxation function.
本文提出了弛豫的等待-切换随机模型。利用概率论极限定理的“随机变量”形式体系，我们解释了复杂系统弛豫响应中短期和长期分数幂律的普遍性。我们表明，宏观系统非平衡态的时间演化取决于两种随机机制：一种决定弛豫实体的局部统计特性，另一种决定微观和介观弛豫贡献的数量（随机或确定性）。在所提出的框架内，我们推导了哈弗里利亚克-内加米函数和科尔劳施-威廉姆斯-瓦特函数。我们还讨论了迁移缺陷的随机游走特性对均匀和非均匀弛豫情形的影响，并展示了系综平均弛豫函数积分表示中拉伸指数积分核的起源。
