Sluggish Kinetics in the Parking Lot Model

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.

7 pages, 5 figures, submitted to J. Phys. A

References in corpus (3)

• Slow relaxation in granular compaction
• Collectiive Properties of Adsorption-Desorption Processes
• Random Sequential Adsorption on a Line: Mean-Field Theory of Diffusional Relaxation

Cited by in corpus (4)

• Chaperone assisted translocation
• Some applications of the Lambert W function to classical statistical mechanics
• The adsorption-desorption model and its application to vibrated granular materials
• Edwards-like statistical mechanical description of the parking lot model for vibrated granular materials