Attractor nonequilibrium stationary states in perturbed long-range interacting systems.
Isolated long-range interacting particle systems appear generically to relax to nonequilibrium states ("quasistationary states" or QSSs) 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 QSSs 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 nonequilibrium stationary state, completely different from 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.
Laboratoire de Physique Nucléaire et de Hautes Énergies, UPMC IN2P3 CNRS UMR 7585, Sorbonne Universités, 4, place Jussieu, 75252 Paris Cedex 05, France.
Michael
M
Joyce
Laboratoire de Physique Nucléaire et de Hautes Énergies, UPMC IN2P3 CNRS UMR 7585, Sorbonne Universités, 4, place Jussieu, 75252 Paris Cedex 05, France.|National Institute for Theoretical Physics (NITheP), Stellenbosch 7600, South Africa.|Institute of Theoretical Physics, Department of Physics, Stellenbosch University, Stellenbosch 7600, South Africa.|Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France.
Jules
J
Morand
Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, Sorbonne Universités, 4 place Jussieu, 75252 Paris Cedex 05, France.
Pascal
P
Viot