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

✍ Scribed by Karina Weron; Marcin Kotulski

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 415 KB
• Volume: 232
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(96)00209-9

✦ Synopsis

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-Lefller distribution. We provide also analytical formulas for the propagators of the nonbiased and biased FTRWs.