AUTHOR=Bao Jing-Dong 

TITLE=Time-Dependent Fractional Diffusion and Friction Functions for Anomalous Diffusion

JOURNAL=Frontiers in Physics

VOLUME=Volume 9 - 2021

YEAR=2021

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2021.567161

DOI=10.3389/fphy.2021.567161

ISSN=2296-424X

ABSTRACT=The precise determination of diffusive properties is presented for a system described by the generalized Langevin equation. The time-dependent fractional diffusion function and GreenKubo relation as well as the generalized Stokes-Einstein formula, in the spirt of ensemble averages, are reconfigured. The effective friction function is introduced as a measure of the influence of a frequency-dependent friction on the evolution of the system. Application to the generalized Debye model, from which self-oscillation emerges as indicative of ergodicity breaking due to cutoff of high finite-frequency. Moreover, several inconsistent conclusions that have appeared in the literature are revived.