Trapped by the drift

TL;DR

This paper explores how constant drift influences diffusion in crowded, fractal-like environments, revealing increased trapping, anisotropy, and complex diffusive behaviors including superdiffusion and subdiffusion.

Contribution

It demonstrates that drift can enhance trapping and subdiffusive signatures, altering the interplay between environment, drift, and diffusion in complex systems.

Findings

Drift increases trapping and anisotropy in diffusion.

High variability in trajectories affects macroscopic diffusive patterns.

Drift can enhance subdiffusive behavior in crowded environments.

Abstract

The diffusion type is determined not only by microscopic dynamics but also by the environment properties. For example, the environment's fractal structure is responsible for the emergence of subdiffusive scaling of the mean square displacement in Markovian systems because the presence of non-trivially placed obstacles puts constraints on possible displacements. We investigate how the additional action of drift changes properties of the diffusion in the crowded environment. It is shown that the action of a constant drift increases chances of trapping, which suppresses the persistent ballistic motion. Such a diffusion becomes anisotropic because the drift introduces a preferred direction of motion which is further altered by interactions with obstacles. Moreover, individual trajectories display a high level of variability, which is responsible for the macroscopic properties of the diffusing front. Overall, the interplay between drift, diffusion and crowded environment, as measured by the time-averaged mean square displacement, is responsible for the emergence of superdiffusive and subdiffusive patterns in the very same system. Importantly, in contrast to free motion, the constant drift can enhance signatures of subdiffusive motion.