Anomalous diffusion of scaled Brownian tracers

• DOI: 10.48550/arxiv.2401.03127
• Publication Date: 2024-01-01
• Authors: Francisco J. Sevilla; Adriano Valdés-Gómez; Alexis Torres-Car...
• Keywords: Anomalous Diffusion; Kurtosis; Mean squared displacement; BETA (programming language)

A model for anomalous transport of tracer particles diffusing in complex media two dimensions is proposed. The takes into account the characteristics persistent motion that active bath transfer to tracer, thus proposed here extends Brownian motion, which stochastic dynamics orientation propelling force described by scale (sBm), identified a time dependent diffusivity form $D_\beta\propto t^{\beta-1}$, $\beta>0$. If $\beta\neq1$, sBm highly non-stationary and suitable describe such non-equilibrium induced media. In this paper we provide analytical calculations computer simulations show genuine diffusion emerge long-time regime, with scaling mean square displacement $t^{2-\beta}$, while ballistic $t^2$, characteristic found short-time one. An analysis dependence kurtosis, intermediate scattering function positions distribution, as well propulsion auto-correlation function, defines effective persistence time, are provided.