MG12 - Talk detail
 

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 Participant 

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Abstract

Collective and microscopic dynamics in mean field Hamiltonian models

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.

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