分数阶动力学的随机游走方法中复合计数过程作用的实验证据
Experimental Evidence of the Role of Compound Counting Processes in Random Walk Approaches to Fractional Dynamics
摘要：
我们目前的介电谱数据获得的镓掺杂镉$_{0.99}$锰$_{0.01}$ Te：镓混合晶体表现出一个非常特殊的情况下的两个幂律松弛模式的高频幂律指数等于1。我们解释了这种行为，这不能拟合没有一个著名的经验松弛函数，在一个从属的扩散框架。我们提出的扩散方案的基础上重新规范化聚类的随机数的时空步骤的连续时间随机游走。这种结构取代了经典的连续时间随机游走方法中使用的更新计数过程，由一个复合计数。结果，我们得到了一个新的弛豫函数的观察到的非标准模式，我们的复合计数过程在研究复杂系统的分数动力学的重要性。
英文摘要：
We present dielectric spectroscopy data obtained for gallium-doped Cd$_{0.99}$Mn$_{0.01}$Te:Ga mixed crystals which exhibit a very special case of the two-power-law relaxation pattern with the high-frequency power-law exponent equal to 1. We explain this behavior, which cannot be fitted by none of the well-known empirical relaxation functions, in a subordinated diffusive framework. We propose diffusion scenario based on a renormalized clustering of random number of spatio-temporal steps in the continuous time random walk. Such a construction substitutes the renewal counting process, used in the classical continuous time random walk methodology, by a compound counting one. As a result, we obtain a novel relaxation function governing the observed non-standard pattern, and we show the importance of the compound counting processes in studying fractional dynamics of complex systems.
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