Abstract
In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis. Using only this property, it can be shown that the response and relaxation functions are non-negative. They are connected to each other and obey the time evolution provided by integral equations involving the memory function M(t), which is the Stieltjes function as well. This fact is also due to the Stieltjes character of the spectral function. Stochastic processes-based approach to the relaxation phenomena gives the possibility to identify the memory function M(t) with the Laplace (Lévy) exponent of some infinitely divisible stochastic processes and to introduce its partner memory k(t). Both memories are related by the Sonine equation and lead to equivalent evolution equations which may be freely interchanged in dependence of our knowledge on memories governing the process.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference31 articles.
1. Broadband Dielectric Spectroscopy;Kremer,2003
2. The universal dielectric response and its physical significance
3. Theory of Electric Polarization;Böttcher,1996
4. Volterra Integral and Functional Equations;Gripenberg,1990
5. Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics
Cited by
6 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献