On the Cole-Cole relaxation function and related Mittag-Leffler distribution

被引：121

作者：

Weron, K ^{[1
]}

Kotulski, M ^{[1
]}

机构：

[1] WROCLAW TECH UNIV, HUGO STEINHAUS CTR STOCHAST METHODS, PL-50370 WROCLAW, POLAND

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 1996年 / 232卷 / 1-2期

关键词：

relaxation; random walks; Levy-stable distributions;

D O I：

10.1016/0378-4371(96)00209-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In the framework of the one-dimensional fractal time random walk (FTRW) relaxation model, we rigorously show that the frequency domain response takes, in both nonbiased and biased walks, the only possible Cole-Cole form. The underlying reason for this is the specific form of the relaxation function (the survival probability of a relaxing system) determined in this model by the Mittag-Leffler distribution. We provide also analytical formulas for the propagators of the nonbiased and biased FTRWs.

引用

页码：180 / 188

页数：9

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