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Kinetic theory of collisionless relaxation for systems with long-range interactions

Dec 21, 2021
Published in:
  • Physica A 606 (2022) 128089
  • Published: Nov 15, 2022
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Abstract: (Elsevier B.V.)
We develop the kinetic theory of collisionless relaxation for systems with long-range interactions in relation to the statistical theory of Lynden-Bell. We treat the multi-level case. We make the connection between the kinetic equation obtained from the quasilinear theory of the Vlasov equation and the relaxation equation obtained from a maximum entropy production principle. We propose a method to close the infinite hierarchy of kinetic equations for the phase level moments and obtain a kinetic equation for the coarse-grained distribution function in the form of a generalized Landau, Lenard–Balescu or Kramers equation associated with a generalized form of entropy (Chavanis, 2004). This allows us to go beyond the two-level case associated with a Fermi–Dirac-type entropy. We discuss the numerous analogies with two-dimensional turbulence. We also mention possible applications of the present formalism to fermionic and bosonic dark matter halos.
  • Collisionless relaxation
  • Lynden-Bell statistical theory
  • Vlasov equation
  • Kinetic theory
  • Generalized entropy
  • Dynamical stability
  • [1]
    DauxoisT.RuffoS.ArimondoE.WilkensM
      • Lectures Notes in Physics vol. 602 (2002)
  • [2]
    CampaA.GiansantiA.MorigiG.Sylos LabiniF
      • AIP Conf.Proc. 965 (2008) 122
  • [3]
    DauxoisT.RuffoS.CugliandoloL
  • [4]
    • A. Campa
      ,
    • T. Dauxois
      ,
    • S. Ruffo
      • Phys. Rep. 480 (2009) 57
  • [5]
    • A. Campa
      ,
    • T. Dauxois
      ,
    • D. Fanelli
      ,
    • S. Ruffo
  • [6]
    • A. Lenard
      • Annals Phys. 10 (1960) 390
  • [7]
    • R. Balescu
      • Phys.Fluids 3 (1960) 52
  • [8]
    • J. Heyvaerts
      • Mon. Not. R. Astron. Soc. 407 (2010) 355
  • [9]
    • P.H. Chavanis
      • Physica A 391 (2012) 3680
  • [10]
    • L.D. Landau
      • Phys. Z. Sowj. Union 10 (1936) 154
  • [12]
    • P.H. Chavanis
      • Eur.Phys.J.Plus 127 (2012) 19
  • [13]
    • S. Chandrasekhar
  • [14]
    • J.B. Fouvry
      ,
    • B. Bar-Or
      ,
    • P.H. Chavanis
      • Phys.Rev.E 100 (2019) 052142
  • [15]
    • J.B. Fouvry
      ,
    • P.H. Chavanis
      ,
    • C. Pichon
      • Phys.Rev.E 102 (2020) 052110
  • [16]
    • J.H. Jeans
      • Mon. Not. R. Astron. Soc. 76 (1915) 70
  • [17]
    • A.A. Vlasov
      • Zh. Eksp. I Teor. Fiz. 8 (1938) 291
  • [19]
    • M. Hénon
      • Ann. Astrophys. 27 (1964) 83
  • [20]
    DauxoisT.RuffoS.ArimondoE.WilkensM
    • P.H. Chavanis
      • Lect.Notes Phys. (2002)
  • [21]
    • F. Bouchet
      ,
    • A. Venaille
      • Phys. Rep. 515 (2012) 227
  • [22]
    • D. Lynden-Bell
      • Mon. Not. R. Astron. Soc. 136 (1967) 101
  • [23]
    • J. Miller
      • Phys.Rev.Lett. 65 (1990) 2137
  • [24]
    • R. Robert
      ,
    • J. Sommeria
      • J.Fluid Mech. 229 (1991) 291
  • [25]
    (Ph.D. thesis)Analogie avec la relaxation violente des systèmes stellaires, Ecole Normale Supérieure de Lyon
    • P.H. Chavanis