Large Deviations in One-Dimensional Random Sequential Adsorption

Abstract

In random sequential adsorption (RSA), objects are deposited randomly, irreversibly, and sequentially; attempts leading to an overlap with previously deposited objects are discarded. The process continues until the system reaches a jammed state when no further additions are possible. We analyze a class of lattice RSA models in which landing on an empty site in a segment is allowed when at least $b$ neighboring sites on the left and the right are unoccupied. For the minimal model ($b=1$), we compute the full counting statistics of the occupation number. We reduce the determination of the full counting statistics to a Riccati equation that appears analytically solvable only when $b=1$. We develop a perturbation procedure which, in principle, allows one to determine cumulants consecutively, and we compute the variance of the occupation number for all $b$.

arXiv comment11 pages, 2 figures

References in corpus (22)

• Probing many-body dynamics on a 51-atom quantum simulator
• Fast quantum gates for neutral atoms
• Quantum many-body scars
• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• Quantum scarred eigenstates in a Rydberg atom chain: entanglement, breakdown of thermalization, and stability to perturbations
• Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approach
• Signatures of integrability in the dynamics of Rydberg-blockaded chains
• Full counting statistics and phase diagram of a dissipative Rydberg gas
• Full counting statistics of laser excited Rydberg aggregates in a one-dimensional geometry
• Complex density wave orders and quantum phase transitions in a model of square-lattice Rydberg atom arrays
• Sub-Poissonian statistics of Rydberg-interacting dark-state polaritons
• Cooperative excitation and many-body interactions in a cold Rydberg gas
• Entropic enhancement of spatial correlations in a laser-driven Rydberg gas
• Jamming, freezing and metastability in one-dimensional spin systems
• Exact Solution of a Phase Separation Model with Conserved Order Parameter Dynamics
• Parking on a Random Tree
• Wireless network control of interacting Rydberg atoms
• Exact steady-state velocity of ratchets driven by random sequential adsorption
• Fluctuations in Polymer Translocation
• Generalized random sequential adsorption on Erdős-Rényi random graphs
• Scaling Limits and Generic Bounds for Exploration Processes
• Universality in survivor distributions: Characterising the winners of competitive dynamics

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• Birds on a Wire
• On the structure factor of jammed particle configurations on the one-dimensional lattice
• Dynamic Space Packing
• Random sequential covering of a one-dimensional lattice by $k$-mers