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Time-Dependent Fractional Diffusion and Friction Functions for Anomalous Diffusion
Frontiers in Physics ( IF 3.1 ) Pub Date : 2021-01-05 , DOI: 10.3389/fphy.2021.567161
Jing-Dong Bao

The precise determination of diffusive properties is presented for a system described by the generalized Langevin equation. The time-dependent fractional diffusion function and the Green-Kubo relation as well as the generalized Stokes-Einstein formula, in the spirit of ensemble averages, are reconfigured. The effective friction function is introduced as a measure of the influence of frequency-dependent friction on the evolution of the system. This is applied to the generalized Debye model, from which self-oscillation emerges as indicative of ergodicity that breaks due to high finite-frequency cutoff. Moreover, several inconsistent conclusions that have appeared in the literature are revised.



中文翻译:

依赖时间的分数阶扩散和摩擦函数

给出了由广义Langevin方程描述的系统的扩散特性的精确确定。按照集合平均的精神,重新构造了随时间变化的分数扩散函数和Green-Kubo关系以及广义的Stokes-Einstein公式。引入了有效摩擦函数,作为对频率相关摩擦对系统演化的影响的度量。这被应用于广义的德拜模型,从中出现自激振荡,表明由于高有限频率截止而使遍历性破裂。此外,对文献中出现的一些不一致的结论进行了修订。

更新日期:2021-02-19
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