Transport with hard-core interaction in a chain of asymmetric cavities

TL;DR

This study explores how particle diffusion in asymmetric cavities is affected by hard-core interactions and external forces, revealing concentration-dependent effects and proposing a modified Fick-Jacobs equation for analytical description.

Contribution

The paper introduces a modified Fick-Jacobs equation to analytically model particle transport with hard-core interactions in asymmetric cavities, supported by numerical verification.

Findings

Current difference depends on particle concentration.

Hard-core interactions vanish and invert asymmetry at high concentrations.

Analytical results agree well with numerical simulations.

Abstract

In this paper we investigate the diffusion of particles inside a chain of asymmetric cavities. We are considering particles that interact through a hard--core potential and are driven by an external force. We show that the difference in the current when the force is applied to the left and to the right strongly depends on the concentration inside the cavity. We found that, when the concentration is high enough, the hard--core interaction vanishes and inverts the asymmetric effect of the cavity. We also introduce a new equation, a modification to the Fick--Jacobs equation, to describe this system analytically. Finally, we used numerical simulations to verify the analytic results, finding a good agreement between theory and simulations.