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Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions (Articolo in rivista)

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Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions (Articolo in rivista) (literal)

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Bruno Marcos (1,2); Andrea Gabrielli (2,3); Michael Joyce (4,5) (2012)
Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions
in Central European Journal of Physics (Print)
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1. Laboratoire J.-A. Dieudonné, UMR 6621, Université de Nice -- Sophia Antipolis, Parc Valrose, 06108, Nice Cedex 02, France 2. SMC, CNR-INFM, Physics Department, University \"Sapienza\" of Rome, Piazzale Aldo Moro 2, 00185, Rome, Italy 3. Istituto dei Sistemi Complessi -- CNR, Via dei Taurini 19, 00185, Rome, Italy 4. Laboratoire de Physique Nucléaire et Hautes Énergies, Université Pierre et Marie Curie -- Paris 6, CNRS IN2P3 UMR 7585, 4 Place Jussieu, 75752, Paris Cedex 05, France 5. Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie -- Paris 6, CNRS UMR 7600, 4 Place Jussieu, 75752, Paris Cedex 05, France (literal)

Titolo

Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions (literal)

Abstract

Systems of particles interacting with long range interactions present generically \"quasi-stationary states\" (QSS), which are approximately time-independent out of equilibrium states. In this proceedings, we explore the generalization of the formation of such QSS and their relaxation from the much studied case of gravity to a generic pair interaction with the asymptotic form of the potential v(r) similar to 1/r (gamma) with gamma > 0 in d dimensions. We compute analytic estimations of the relaxation time calculating the rate of two body collisionality in a virialized system approximated as homogeneous. We show that for gamma < (d - 1/2), the collision integral is dominated by the size of the system, while for gamma > (d - 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles if gamma < d - 1 (i.e. the force is not integrable) and decreases if gamma > d - 1. Using numerical simulations we confirm our analytic results. A corollary of our work gives a \"dynamical\" classification of interactions: the dynamical properties of the system depend on whether the pair force is integrable or not. (literal)

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