Exploring the thermodynamic limit of Hamiltonian models: Convergence to the Vlasov equation

Andrea Antoniazzi, Francesco Califano, Duccio Fanelli, Stefano Ruffo

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We here discuss the emergence of quasistationary states (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian mean-field model, numerical simulations are performed based on both the original N-body setting and the continuum Vlasov model which is supposed to hold in the thermodynamic limit. A detailed comparison unambiguously demonstrates that the Vlasov-wave system provides the correct framework to address the study of QSS. Further, analytical calculations based on Lynden-Bell's theory of violent relaxation are shown to result in accurate predictions. Finally, in specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particle correlations. © 2007 The American Physical Society.
    Original languageEnglish
    Article number150602
    JournalPhysical Review Letters
    Volume98
    Issue number15
    DOIs
    Publication statusPublished - 12 Apr 2007

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