NonDebye relaxations: The characteristic exponent in the excess wings model
Abstract
The characteristic (Laplace or Lévy) exponents uniquely characterize infinitely divisible probability distributions. Although of purely mathematical origin they appear to be uniquely associated with the memory functions present in evolution equations which govern the course of such physical phenomena like nonDebye relaxations or anomalous diffusion. Commonly accepted procedure to mimic memory effects is to make basic equations time smeared, i.e., nonlocal in time. This is modeled either through the convolution of memory functions with those describing relaxation/diffusion or, alternatively, through the time smearing of time derivatives. Intuitive expectations say that such introduced time smearings should be physically equivalent. This leads to the conclusion that both kinds of so far introduced memory functions form a "twin" structure familiar to mathematicians for a long time and known as the Sonine pair. As an illustration of the proposed scheme we consider the excess wings model of nonDebye relaxations, determine its evolution equations and discuss properties of the solutions.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.07415
 Bibcode:
 2021arXiv210907415G
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Mathematical Physics
 EPrint:
 Commun. Nonlinear Sci. Numer. Simulat., 103 (2021) 106006