Relaxation of quasi-stationary states in long range interacting systems and a classification of the range of pair interactions |
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Authors: | Bruno Marcos Andrea Gabrielli Michael Joyce |
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Institution: | 1.Laboratoire J.-A. Dieudonné, UMR 6621,Université de Nice — Sophia Antipolis,Nice Cedex 02,France;2.SMC, CNR-INFM, Physics Department,University “Sapienza” of Rome,Rome,Italy;3.Istituto dei Sistemi Complessi — CNR,Rome,Italy;4.Laboratoire de Physique Nucléaire et Hautes énergies,Université Pierre et Marie Curie — Paris 6, CNRS IN2P3 UMR 7585,Paris Cedex 05,France;5.Laboratoire de Physique Théorique de la Matière Condensée,Université Pierre et Marie Curie — Paris 6, CNRS UMR 7600,Paris Cedex 05,France |
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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) ∼ 1/r
γ
with γ > 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 γ < (d − 1/2), the collision integral is dominated by the size of the system, while for γ > (d − 1/2), it is dominated by small impact parameters. In addition, the lifetime of QSS increases with the number of particles
if γ < d − 1 (i.e. the force is not integrable) and decreases if γ > 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. |
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