Modeling Rydberg gases using random sequential adsorption on random graphs

The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay two factors: geometrical restrictions induced blockade effects, and quantum mechanical effects. To shed light on their relative roles in gases, we compare three models this paper: a model describing excitation dynamics within gas, Random Sequential Adsorption (RSA) process Geometric Graph (RGG), RSA Decomposed Intersection (DRIG). latter is new, refers to choosing particular subgraph mixture other random graphs. Contrary former models, it lends itself for rigorous mathematical analysis; built specifically have structural properties RGG. We establish fluid limit time-evolution number atoms, show numerically that expression remains accurate across wider range particle densities than an earlier approach based Erdos-Renyi (ERRG). Finally, also come up with new heuristic using graphs gives recursion describe normalized pair-correlation function gas. Our results suggest even without dissipation, long time scales affected most while short