Power-law decay in first-order relaxation processes

Abstract

Starting from a simple definition of stationary regime in first-order relaxation processes, we obtain that experimental results are to be fitted to a power-law when approaching the stationary limit. On the basis of this result we propose a graphical representation that allows the discrimination between power-law and stretched exponential time decays. Examples of fittings of magnetic, dielectric and simulated relaxation data support the results. 76.20.+q, 76.90.+d, 75.40.Mg

A new approach to diffusion-like relaxation processes

“…Then, in order to get to a reference point, we hypothesize that the physics governing the evolution are diffusion-like, i.e., the time derivative of the interaction that describes the microscopic state of the sample depends on the spatial-like dependence of that interaction (let us say, dependence on spatial coordinates or other coordinates used for the description of the material). In such a generic case, which covers many of the possible scenarios in solids, we have demonstrated analytically that the decay should end up by following this power law [3]:…”

“…1(a), we show the time decay of the electric field vs. time in acetal. Our way to explore the data is to replot them in the form dE/d ln t vs. E [3]. With this, the whole relaxation process can be viewed in a finite window.…”

“…We have recently proposed new ideas to identify correctly under which law a relaxation is produced [3]. In this paper, we are studying the dielectric relaxation of two types of non-crystalline solids under this approach, in order to try to infer anything about the nature of the interaction that describes their evolution in time.…”

Complex oxide acousto-electronics

“…The inset shows the same data on a logarithmic time scale. The quasi linear trend of the SAW signals versus time on a double log-scale suggest a power-law decay consistent with thermal relaxation processes 78,91 . The same trend was also obtained for other LED wavelengths.…”

“…One is photoconductivity, which is a consequence of electron excitation to the conduction band from the valance band due to absorption of photons with an energy higher than the optical band gap 90 . The other is accelerated oxygen vacancy migration under illumination with visible light 91 . Migration of charged defects such as oxygen vacancies under application of an electric field contributes to the polarization of STO, where the timescale for saturation of the polarization should depend on the mobility of the oxygen vacancies and the applied field strength 89 .…”