# Sluggish Kinetics in the Parking Lot Model

Source: [Sluggish Kinetics in the Parking Lot Model](<https://www.sota2.com/research/paper/68fa24992c2a3760193a6567>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:20:15.324Z

Authors: J. Talbot, G. Tarjus, P. Viot

Published: 1998-09-24T09:35:48.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9809326>)

[PDF](<https://arxiv.org/pdf/cond-mat/9809326.pdf>)