Eur. Phys. J. B 29, 577-591 (2002)
https://doi.org/10.1140/epjb/e2002-00342-3

Birth and long-time stabilization of out-of-equilibrium coherent structures

¹ Laboratoire de Physique (UMR-CNRS 5672) , ENS Lyon, 46 Allée d'Italie, 69364 Lyon Cedex 07, France
² Dipartimento di Energetica “S. Stecco”, Università di Firenze, via S. Marta, 3, 50139 Firenze, Italy
³ Institut Fourier (UMR 5582) , BP 74, 38402 Saint Martin d'Hères Cedex, France
⁴ INFM and INFN, Firenze, Italy

Corresponding author: ^a Thierry.Dauxois@ens-lyon.fr

Received: 28 February 2002
Revised: 24 July 2002
Published online: 31 October 2002

Abstract

We study an analytically tractable model with long-range interactions for which an out-of-equilibrium very long-lived coherent structure spontaneously appears. The dynamics of this model is indeed very peculiar: a bicluster forms at low energy and is stable for very long time, contrary to statistical mechanics predictions. We first explain the onset of the structure, by approximating the short time dynamics with a forced Burgers equation. The emergence of the bicluster is the signature of the shock waves present in the associated hydrodynamical equations. The striking quantitative agreement with the dynamics of the particles fully confirms this procedure. We then show that a very fast timescale can be singled out from a slower motion. This enables us to use an adiabatic approximation to derive an effective Hamiltonian that describes very well the long time dynamics. We then get an explanation of the very long time stability of the bicluster: this out-of-equilibrium state corresponds to a statistical equilibrium of an effective mean-field dynamics.