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  • Scaling with system size of the Lyapunov exponents for the Hamiltonian Mean Field model
    Manos, Thanos ; Ruffo, Stefano
    The Hamiltonian Mean Field model is a prototype for systems with long-range interactions. It describes the motion of N particles moving on a ring, coupled with an infinite-range potential. The model ... has a second-order phase transition at the energy density Uc =3/4 and its dynamics is exactly described by the Vlasov equation in the NŽŽ limit. Its chaotic properties have been investigated in the past, but the determination of the scaling with N of the Lyapunov Spectrum (LS) of the model remains a challenging open problem. Here we show that the N Ž1/3 scaling of the Maximal Lyapunov Exponent (MLE), found in previous numerical and analytical studies, extends to the full LS; scaling is "precocious" for the LS, meaning that it becomes manifest for a much smaller number of particles than the one needed to check the scaling for the MLE. Besides that, the N 1/3 scaling appears to be valid not only for U>Uc , as suggested by theoretical approaches based on a random matrix approximation, but also below a threshold energy Ut 0.2. Using a recently proposed method (GALI) devised to rapidly check the chaotic or regular nature of an orbit, we find that Ut is also the energy at which a sharp transition from weak to strong chaos is present in the phase-space of the model. Around this energy the phase of the vector order parameter of the model becomes strongly time dependent, inducing a significant untrapping of particles from anonlinear resonance.
    Source: Papers from Vlasovia 2009 - Part 2 : international workshop on the theory and applications of Vlasov equations : Marseilles, France, 31 August - 4 September 2009 (Vol. 40, issue 6/7, 2011, str. 360-381)
    Type of material - conference contribution
    Publish date - 2011
    Language - english
    COBISS.SI-ID - 73838337

    Link(s):

    http://www.tandfonline.com/doi/full/10.1080/00411450.2011.651035
    http://apps.webofknowledge.com/full_record.do?product=WOS&search_mode=GeneralSearch&qid=25&SID=N1PdAoEAFhDmgJlBe9c&page=1&doc=1
    DOI

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