# Relaxation Processes in Long-Range Lattices

## TL;DR

This paper investigates how long-range interactions affect the relaxation times in lattice systems, revealing polynomial scaling with system size and the importance of non-Markovian effects in the relaxation process.

## Contribution

It introduces a kinetic equation for long-range lattices that explains the observed timescales and interaction thresholds, highlighting the role of non-Markovian effects.

## Key findings

- Relaxation times scale polynomially with system size.
- A kinetic equation explains the interaction range threshold.
- Non-Markovian effects significantly influence relaxation dynamics.

## Abstract

The relaxation to equilibrium of lattice systems with long-range interactions is investigated. The timescales involved depend polynomially on the system size, potentially leading to diverging equilibration times. A kinetic equation for long-range lattices is proposed, which explain these timescales as well as a threshold in the interaction range reported in [Phys. Rev. Lett. 110, 170603 (2013)]. Non-Markovian effects are shown to play an important role in the relaxation of systems of up to thousands of particles.