Microscopic theory for negative differential mobility in crowded environments

TL;DR

This paper presents an analytical lattice gas model showing that a driven particle's velocity in crowded environments can decrease with increasing force, revealing conditions for negative differential mobility (NDM) in various physical systems.

Contribution

It provides a unified analytical framework for understanding NDM, linking it to obstacle density and diffusion time scales, and identifies the parameter space where NDM occurs.

Findings

NDM occurs at specific obstacle densities and force regimes.

Analytical expressions predict the onset of NDM.

Results unify previous numerical and analytical studies.

Abstract

We study the behavior of the stationary velocity of a driven particle in an environment of mobile hard-core obstacles. Based on a lattice gas model, we demonstrate analytically that the drift velocity can exhibit a nonmonotonic dependence on the applied force, and show quantitatively that such negative differential mobility (NDM), observed in various physical contexts, is controlled by both the density and diffusion time scale of obstacles. Our study unifies recent numerical and analytical results obtained in specific regimes, and makes it possible to determine analytically the region of the full parameter space where NDM occurs. These results suggest that NDM could be a generic feature of biased (or active) transport in crowded environments.