Time-Dependent Fractional Diffusion and Friction Functions for Anomalous Diffusion - Bao, Jing-Dong (Frontiers in Physics, 2021)
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.