Aurelio Patelli, Università di Firenze #
Linear response theory for long range interacting systems #
Long-range interacting systems, while relaxing to equilibrium, often get 
trapped in long-
lived quasistationary states which have lifetimes that diverge with the 
system size. In this
work, we address the question of how a long-range system in a 
quasistationary state (QSS)
responds to an external perturbation. We consider a long-range system that 
evolves under
deterministic Hamilton dynamics. The perturbation is taken to couple to 
the canonical
coordinates of the individual constituents. Our study is based on 
analyzing the Vlasov
equation for the single-particle phase space distribution. The QSS 
represents stable sta-
tionary solution of the Vlasov equation in the absence of the external 
perturbation. In
the presence of small perturbation, we linearize the perturbed Vlasov 
equation about the
QSS to obtain a formal expression for the response observed in a 
single-particle dynami-
cal quantity. We apply our analysis to a paradigmatic model, the 
Hamiltonian mean-field
model, that involves particles moving on a circle under Hamilton dynamics. 
Our prediction
for the response of some representative QSSs in this model (the water-bag 
QSS and the
Gaussian QSS) is found to be in good agreement with N-particle simulations 
for large N.