On the Glassy Behavior of Parking Lot Model

TL;DR

This paper provides a theoretical analysis of the reversible parking problem, revealing its glassy behavior through dual time scales and aligning well with simulation data, offering insights into granular compaction and glassy systems.

Contribution

It introduces a theoretical framework explaining glassy dynamics in the parking model, emphasizing the role of two distinct time scales and collective processes.

Findings

Identification of two key time scales in the parking model.

Good agreement between theory and simulation data.

Insights into granular compaction and glassy behavior.

Abstract

We present a theoretical discussion of the reversible parking problem, which appears to be one of the simplest systems exhibiting glassy behavior. The existence of slow relaxation, nontrivial fluctuations, and an annealing effect can all be understood by recognizing that two different time scales are present in the problem. One of these scales corresponds to the fast filling of existing voids, the other is associated with collective processes that overcome partial ergodicity breaking. The results of the theory are in a good agreement with simulation data; they provide a simple qualitative picture for understanding recent granular compaction experiments and other glassy systems.