Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation.

Dipartimento di Energetica and CSDC, Università di Firenze, and INFN, via S. Marta, 3, 50139 Firenze, Italy.
Physical Review Letters (Impact Factor: 7.73). 05/2007; 98(15):150602. DOI: 10.1103/PHYSREVLETT.98.150602
Source: PubMed

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.

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