Complexity Function of Jammed Configurations of Rydberg Atoms

TL;DR

This paper calculates the configurational entropy of jammed Rydberg atom arrangements on a 1D lattice, deriving explicit formulas and linking to deposition models, advancing understanding of their combinatorial complexity.

Contribution

It introduces a method to compute the complexity of jammed Rydberg configurations using combinatorial and optimization techniques, providing explicit formulas related to the blockade range.

Findings

Complexity expressed via roots of a polynomial depending on blockade range

Explicit asymptotic formulas for the number of jammed configurations

Connection established between Rydberg atom arrangements and k-mer deposition models

Abstract

In this article, we determine the complexity function (configurational entropy) of jammed configurations of Rydberg atoms on a one-dimensional lattice. Our method consists of providing asymptotics for the number of jammed configurations determined by direct combinatorial reasoning. In this way we reduce the computation of complexity to solving a constrained optimization problem for the Shannon's entropy function. We show that the complexity can be expressed explicitly in terms of the root of a certain polynomial of degree $b$, where $b$ is the so-called blockade range of a Rydberg atom. Our results are put in a relation with the model of irreversible deposition of $k$-mers on a one-dimensional lattice.