Sluggish Kinetics in the Parking Lot Model

TL;DR

This paper studies the slow relaxation dynamics of a microscopic model of hard rods adsorbing on a line, revealing three distinct kinetic regimes and emphasizing the importance of a gap-distribution approach for accurate predictions.

Contribution

It introduces a systematic gap-distribution method to accurately describe the slow kinetics of the parking lot model, surpassing mean-field approximations.

Findings

Long-time kinetics exhibit three regimes: algebraic, logarithmic, and exponential.

Mean-field approach fails to predict the exponential relaxation rate.

Systematic gap-distribution approach provides correct relaxation dynamics.

Abstract

We investigate, both analytically and by computer simulation, the kinetics of a microscopic model of hard rods adsorbing on a linear substrate. For a small, but finite desorption rate, the system reaches the equilibrium state very slowly, and the long-time kinetics display three successive regimes: an algebraic one where the density varies as $1/t$, a logarithmic one where the density varies as $1/ln(t)$, followed by a terminal exponential approach. A mean-field approach fails to predict the relaxation rate associated with the latter. We show that the correct answer can only be provided by using a systematic description based on a gap-distribution approach.