Scaling quasi-stationary states in long range systems with dissipation

Abstract

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.

5 pages, 3 figures, to appear in Phys. Rev. Lett

References in corpus (10)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Collisionless relaxation in non-neutral plasmas
• The Inelastic Maxwell Model
• Kinetics of a frictional granular motor
• Quasi-stationary states and the range of pair interactions
• Relaxation to thermal equilibrium in the self-gravitating sheet model
• Statistical Mechanics of 1d Self-Gravitating Systems: The Core-Halo Distribution
• Microcanonical quasi-stationarity of long-range interacting systems in contact with a heat bath
• Long-range gravitational-like interaction in a neutral atomic cold gas
• Formation of density singularities in ideal hydrodynamics of freely cooling inelastic gases: a family of exact solutions

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