Doˇsli´c, T., Puljiz, M., ˇSebek, S., & ˇZubrini´c, J. (2024). A model of random sequential adsorption on a ladder graph. arXiv preprint arXiv:2312.02747v3.
This paper investigates the properties of random sequential adsorption (RSA) on a two-row square ladder graph, focusing on the differences between the dynamic model (sequential irreversible deposition) and the equilibrium model (uniform distribution of jammed configurations). The study aims to derive analytical expressions for key statistical measures in both models and compare their behavior, particularly as the blockade range (minimum distance between adsorbed particles) increases.
The authors employ analytical techniques from statistical mechanics and combinatorics. For the dynamic model, they develop a recursive approach to calculate the jamming limit, which represents the average density of adsorbed particles in a jammed configuration. For the equilibrium model, they utilize a bivariate generating function approach to enumerate jammed configurations and derive the complexity function, which describes the exponential growth rate of the number of configurations with a specific density.
The research highlights the distinct behaviors of dynamic and equilibrium models in RSA on a ladder graph, particularly for large blockade ranges. The findings contribute to a deeper understanding of jamming phenomena in constrained geometries and have implications for various physical systems, including Rydberg atom ensembles.
This work extends the theoretical understanding of RSA models beyond one-dimensional systems and provides valuable insights into the interplay between dynamic and equilibrium properties in constrained adsorption processes. The analytical results and comparative analysis offer a framework for studying similar models with potential applications in diverse fields, including physics, chemistry, and materials science.
The study focuses on a specific graph structure (two-row square ladder). Exploring RSA on more complex graphs, considering non-integral blockade ranges, and incorporating additional realistic features (e.g., interactions between adsorbed particles) are potential avenues for future research.
To Another Language
from source content
arxiv.org
Deeper Inquiries