Novel Dynamics and Thermodynamics in systems with long range interactions

TL;DR

This paper introduces a new Hamiltonian model inspired by two-dipole interactions to study long-range systems, revealing novel quasi-stationary states and ensemble nonequivalence through analytical and molecular dynamics analyses.

Contribution

It presents a new Hamiltonian model with an analytical equilibrium solution and explores nonequilibrium quasi-stationary states caused by long-range interactions.

Findings

Analytical equilibrium solution matches simulations.

Observation of long-lived quasi-stationary states.

Evidence of ensemble nonequivalence in long-range systems.

Abstract

Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial conditions that are used here. We present in this letter a new Hamiltonian whose potential is inspired in the two-dipole interaction. An analytical solution is obtained for the equilibrium in the canonical ensemble that is coincident with the one obtained from computational simulations. However, results from this model presents a kind of nonequivalence of ensembles in long-living states before arriving to equilibrium. Thus, a complete characterization is made for the nonequilibrium through molecular dynamics. In which, novel quasi-stationary states are observed due to the long range interactions.