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Scaling quasi-stationary states in long range systems with dissipation

Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such systems in the presence of dissipation. Using an appropriate mean-field kinetic description, we show that models with dissipation due to a viscous damping or due to inelastic collisions admit "scaling quasi-stationary states", i.e., states which are quasi-stationary in rescaled variables. A numerical study of one dimensional self-gravitating systems confirms both the relevance of these solutions, and gives indications of their regime of validity in line with theoretical predictions. We underline that the velocity distributions never show any tendency to evolve towards a Maxwell-Boltzmann form.