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.

Exploring the thermodynamic limit of Hamiltonian models: Convergence to the Vlasov equation / Antoniazzi, A; Califano, F; Fanelli, D; Ruffo, S. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 98:(2007), pp. 1-4. [10.1103/PhysRevLett.98.150602]

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

Ruffo, S
2007-01-01

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
98
1
4
150602
https://arxiv.org/abs/cond-mat/0612219
Antoniazzi, A; Califano, F; Fanelli, D; Ruffo, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12235
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