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Journal
2012 | 10 | 3 | 676-683
Article title

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

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Languages of publication
EN
Abstracts
EN
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.
Publisher
Journal
Year
Volume
10
Issue
3
Pages
676-683
Physical description
Dates
published
1 - 6 - 2012
online
17 - 6 - 2012
References
  • [1] A. Campa, T. Dauxois, S. Ruffo, Phys. Rep. 480, 57 (2009) http://dx.doi.org/10.1016/j.physrep.2009.07.001[Crossref]
  • [2] I. Ispolatov, E. G.D. Cohen, Phys. Rev. E 64, 056103 (2001) http://dx.doi.org/10.1103/PhysRevE.64.056103[Crossref]
  • [3] J. Binney, S. Tremaine, Galactic Dynamics (Princeton University Press, 1994)
  • [4] A. Gabrielli, M. Joyce, B. Marcos, Phys. Rev. Lett. 105, 210602 (2010) http://dx.doi.org/10.1103/PhysRevLett.105.210602[Crossref]
  • [5] A. Gabrielli, M. Joyce, B. Marcos, F. Sicard, J. Stat. Phys. 141, 970 (2010) http://dx.doi.org/10.1007/s10955-010-0090-x[Crossref]
  • [6] M. Kac, G. E. Uhlenbeck, P. C. Hemmer, J. Math. Phys. 4, 216 (1963) http://dx.doi.org/10.1063/1.1703946[Crossref]
  • [7] S. Chandrasekhar, Chicago, The University of Chicago press (1942)
  • [8] M. Hénon, Annales d’Astrophysique 21, 186 (1958)
  • [9] V. Springel, Mon. Not. R. Astron. Soc 364, 1105 (2005) http://dx.doi.org/10.1111/j.1365-2966.2005.09655.x[Crossref]
  • [10] J. Diemand, B. Moore, J. Stadel, S. Kazantzidis, Mon. Not. R. Astron. Soc. 348, 977 (2004) http://dx.doi.org/10.1111/j.1365-2966.2004.07424.x[Crossref]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-012-0032-0
Identifiers
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