Anomalous diffusion of scaled Brownian tracers.

Area of Science:

• Statistical Physics
• Complex Systems
• Soft Matter Physics

Background:

• Anomalous transport in complex media is crucial for understanding diffusion processes.
• Active Brownian motion models particle movement influenced by self-propulsion.
• Scaled Brownian motion (sBm) describes time-dependent diffusivity, D_{β}∝t^{β-1}, suitable for non-equilibrium dynamics.

Purpose of the Study:

• To propose a novel model for anomalous transport of tracer particles in two-dimensional complex media.
• To extend active Brownian motion by incorporating scaled Brownian motion for persistent tracer motion.
• To analyze the emergent anomalous diffusion and transport regimes.

Main Methods:

• Development of a theoretical model incorporating scaled Brownian motion.
• Analytical calculations to derive transport properties.
• Computer simulations to validate theoretical predictions.

Main Results:

• Genuine anomalous diffusion with mean-squared displacement scaling of t^{2-β} in the long-time regime.
• Ballistic transport with t^{2} scaling observed in the short-time regime.
• Analysis of kurtosis, intermediate scattering function, and propulsion autocorrelation.

Conclusions:

• The proposed model accurately describes anomalous transport in complex media.
• The interplay between persistent motion and time-dependent diffusivity leads to distinct short- and long-time transport regimes.
• The model provides a framework for studying non-equilibrium dynamics in active systems.