Out-of-equilibrium dynamics in systems with long-range interactions: characterizing quasi-stationary states

TL;DR

This paper reviews recent theories on the out-of-equilibrium quasi-stationary states in long-range interacting systems, highlighting the gap between theoretical predictions and numerical simulation results.

Contribution

It provides a comprehensive review of existing theories on quasi-stationary states in long-range interactions and discusses their limitations in explaining simulation outcomes.

Findings

Multiple theories exist but none fully explain the dynamics.

Numerical simulations show complex behavior not captured by current theories.

The transition between magnetized and non-magnetized states remains not fully understood.

Abstract

Systems with long-range interactions (LRI) display unusual thermodynamical and dynamical properties that stem from the non-additive character of the interaction potential. We focus in this work on the lack of relaxation to thermal equilibrium when a LRI system is started out-of-equilibrium. Several attempts have been made at predicting the so-called quasi-stationary state (QSS) reached by the dynamics and at characterizing the resulting transition between magnetized and non-magnetized states. We review in this work recent theories and interpretations about the QSS. Several theories exist but none of them has provided yet a full account of the dynamics found in numerical simulations.