Attractor non-equilibrium stationary states in perturbed long-range interacting systems

TL;DR

This study investigates how simple local perturbations influence long-range interacting systems, revealing that such perturbations lead to a universal non-equilibrium stationary state independent of initial conditions.

Contribution

The paper demonstrates that local perturbations in long-range systems cause convergence to a unique QSS, altering the system's long-term behavior and robustness.

Findings

Perturbations drive different QSS towards a single universal state.

The resulting stationary state depends on the perturbations and long-range forces.

The state remains stable even after removing the perturbations.

Abstract

Isolated long-range interacting particle systems appear generically to relax to non-equilibrium states ("quasi-stationary states" or QSS) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSS we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique non-equilibrium stationary state, completely different to its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g. spatial density or velocity distribution) of the system itself.