On the application of Mittag-Leffler functions to hyperbolic-type decay of luminescence

TL;DR

This paper generalizes the Becquerel decay law for luminescence decay using Mittag-Leffler functions with logarithmic arguments, providing a new mathematical framework and discussing its physical implications.

Contribution

It introduces a novel generalization of the Becquerel decay law employing Mittag-Leffler functions with logarithmic arguments, enhancing the modeling of luminescence decay.

Findings

Generalized decay law using Mittag-Leffler functions

Provides physical interpretation of the new model

Connects mathematical generalization with experimental results

Abstract

In 1861, Becquerel analyzed the time-resolved luminescence and formulated an empirical hyperbolic-type decay function, which was later named Becquerel decay law. Since then, studies about hyperbolic decays of luminescence have been carried on in different physical contexts. In this paper we generalize the Becquerel decay law by using a Mittag-Leffler function with a logarithmic argument, and discuss its physical interpretation in light of recently published results.