MERCREDI 02 SEPTEMBRE 2009
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Duccio Fanelli
Université de Florence
Italie

Title: Vlasov dynamics and slow relaxation in mean field Hamiltonian models

Abstract: Long-range systems display a fast relaxation towards Quasi--Stationary States
(QSSs), intermediate regimes of the evolution whose lifetime diverges when
increasing the number N of interacting elements. QSSs present a large gallery
of rather peculiar characteristics which mark a clear distinction with
respect to the corresponding equilibrium configurations, eventually attained
for large enough times, when working at finite N. The ubiquity of QSS is also
a puzzling evidence, calling for a unifying theoretical framework. In this
talk, I shall review the QSS phenomenology with reference to specific mean
field models. In particular, I will discuss the presence of
out--of--equilibrium phase transitions separating homogeneous and
in-homogeneous phases. The latter can be traced by resorting to a statistical
mechanics treatment based on the underlying, continuous Vlasov picture.
Microscopically, N-body investigations reveal an abundance of regular
trajectories, associated with invariant tori of the single-particle dynamics.
Interestingly a local trend to integrability is observed as the system size
is increased, an observation that contributes to clarifying the stability of
QSSs and their attractive nature in the thermodynamic limit.