2024/01/06 by Francisco J. Sevilla, Sevilla, Francisco J., Adriano Valdés-Gómez +3
Chemistry · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Electrostatics and Colloid Interactions #FOS: Physical sciences #Micro and Nano Robotics #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2401.03127
openalex publication_date 2024/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A model for anomalous transport of tracer particles diffusing in complex media in two dimensions is proposed. The model takes into account the characteristics of persistent motion that active bath transfer to the tracer, thus the model proposed in here extends active Brownian motion, for which the stochastic dynamics of the orientation of the propelling force is described by scale Brownian motion (sBm), identified by a the time dependent diffusivity of the form Dβ∝ tβ-1, β>0. If β≠1, sBm is highly non-stationary and suitable to describe such a non-equilibrium dynamics induced by complex media. In this paper we provide analytical calculations and computer simulations to show that genuine anomalous diffusion emerge in the long-time regime, with a time scaling of the mean square displacement t2-β, while ballistic transport t2, characteristic of persistent motion, is found in the short-time one. An analysis of the time dependence of the kurtosis, and intermediate scattering function of the positions distribution, as well as the propulsion auto-correlation function, which defines the effective persistence time, are provided.