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Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation | Andrea Antoniazzi
; Francesco Califano
; Duccio Fanelli
; Stefano Ruffo
; | Date: |
13 Apr 2007 | Journal: | Phys Rev Lett, 98 (15), 150602 | 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. | Source: | PubMed, pmid17501330 | Other source: | [GID 944107] cond-mat/0612219 | Services: | Forum | Review | Favorites |
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