Birth and long-time stabilization of out-of-equilibrium
coherent structures
Julien Barre, Freddy Bouchet, Thierry
Dauxois, Stefano Ruffo
Abstract
We study an analytically tractable model with {\it 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 {\it 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.
Europhysical Journal B accepted.
(full text)