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.
Highlights
We show that the physics of this dynamics is governed by an effective particle deposition process where the rates depend on the distance to other deposited particles as a power-law
We have introduced a simple far-from-equilibrium scenario in which a non-trivial relaxation dynamics is driven by power-law interactions that result in rates that depend on the distance to existing excitations as a power-law
We provide a simple model for the deposition process that captures the essential physics
Summary
Self-similar behavior is predicted for the relaxation of a gas of quenched Bose-condensed atoms as a consequence of the existence of non-thermal fixed points [7, 8]. It is argued [9] that many of these characteristics were present during the evolution of the early universe leading to the idea of using cold atomic systems as analogue systems for addressing problems of relevance to cosmology or particle physics. Our results indicate that the characteristic minimal distance between Rydberg excitations — which is often referred to as blockade radius — is not generally a static quantity but can in the presence of dissipation acquire a non-trivial scale-invariant time-dependence
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