Birth and longtime stabilization of outofequilibrium coherent structures
Abstract
We study an analytically tractable model with longrange interactions for which an outofequilibrium very longlived 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 outofequilibrium state corresponds to a statistical equilibrium of an effective meanfield dynamics.
 Publication:

European Physical Journal B
 Pub Date:
 October 2002
 DOI:
 10.1140/epjb/e2002003423
 arXiv:
 arXiv:condmat/0203013
 Bibcode:
 2002EPJB...29..577B
 Keywords:

 05.20.y;
 05.45.a;
 Classical statistical mechanics;
 Nonlinear dynamics and chaos;
 Condensed Matter  Statistical Mechanics;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 European Physical Journal B 29, 577591 (2002)