SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 44: Poster: Statistical Physics

DY 44.6: Poster

Donnerstag, 30. März 2023, 13:00–16:00, P1

Nonergodicity of scaled fractional Brownian motion with nonliner time and space clocks — •Yingjie Liang1,2, Wei Wang2, Andrey G. Cherstvy2, and Ralf Metzler2,31Hohai University — 2University of Potsdam — 3Asia Pacific Center for Theoretical Physics

Experimental evidences show that diffusion processes are not always Brownian motion. It is anomalous diffusion with the mean squared displacement (MSD) being a power law in time, ultraslow diffusion with a logarithmic law, and superfast diffusion with an exponential law. To describe different types of non-Brownion motion in heterogeneous media, this study provides scaled fractional Brownian motion (SFBM) with nonliner time and space clocks. In the Langevin system for the FBM runnning with a nonliner time clock, i.e., the time scaled FBM, the real time is a temporal function of the original times in FBM. For the FBM runnning with a nonliner space clock, i.e., the space scaled FBM, the real position is a nonlinear spatial function of the orginial positions in FBM. The nonergodicity properties of SFBM are quantified based on single particle trajectories of the fractional Brownian motion running with time and space clocks. The simulations are consistent with the general analytical results in specific values of the dominated parameters for the behaviors of the MSD, time averaged mean squared displacement (TAMSD) and aging. Potential applications of these results are encountered in diverse scientific fields, such as biophysical, soft matter and hydrology systems.

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