Self-similar non-equilibrium dynamics of a many-body system with power-law interactions

TL;DR

This paper investigates the non-equilibrium dynamics of many-body systems with power-law interactions, revealing self-similar evolution and scale invariance in Rydberg gases, with a focus on dynamic excitation spacing.

Contribution

It introduces a novel out-of-equilibrium deposition model with power-law rates, connecting theoretical insights to recent cold atomic gas experiments.

Findings

Self-similar evolution of the system over time

Power-law time dependence of particle concentration

Scale invariance of the structure factor

Abstract

The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power-law on the distance to previously deposited particles. This model draws its relevance from recent experimental progress in the domain of cold atomic gases which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration, and results in a scale invariance of the structure factor. Our findings show that in dissipative Rydberg gases out of equilibrium the characteristic distance among excitations --- often referred to as the blockade radius --- is not a static but rather a dynamic quantity.