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Title: Exploring the Thermodynamic Limit of Hamiltonian Models: Convergence to the Vlasov Equation

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.

Authors:
;  [1];  [2];  [1];  [3]
  1. Dipartimento di Energetica and CSDC, Universita di Firenze, and INFN, via S. Marta, 3, 50139 Florence (Italy)
  2. Dipartimento di Fisica 'E.Fermi' and CNISM, Universita di Pisa, Largo Pontecorvo, 3 56127 Pisa (Italy)
  3. (United Kingdom)
Publication Date:
OSTI Identifier:
20951225
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 15; Other Information: DOI: 10.1103/PhysRevLett.98.150602; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN-VLASOV EQUATION; COMPARATIVE EVALUATIONS; CONVERGENCE; CORRELATIONS; FLUCTUATIONS; HAMILTONIANS; INTERACTION RANGE; MATHEMATICAL SPACE; MEAN-FIELD THEORY; NUMERICAL SOLUTION; RELAXATION; SIMULATION

Citation Formats

Antoniazzi, Andrea, Ruffo, Stefano, Califano, Francesco, Fanelli, Duccio, and Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL. Exploring the Thermodynamic Limit of Hamiltonian Models: Convergence to the Vlasov Equation. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.150602.
Antoniazzi, Andrea, Ruffo, Stefano, Califano, Francesco, Fanelli, Duccio, & Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL. Exploring the Thermodynamic Limit of Hamiltonian Models: Convergence to the Vlasov Equation. United States. doi:10.1103/PHYSREVLETT.98.150602.
Antoniazzi, Andrea, Ruffo, Stefano, Califano, Francesco, Fanelli, Duccio, and Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL. Fri . "Exploring the Thermodynamic Limit of Hamiltonian Models: Convergence to the Vlasov Equation". United States. doi:10.1103/PHYSREVLETT.98.150602.
@article{osti_20951225,
title = {Exploring the Thermodynamic Limit of Hamiltonian Models: Convergence to the Vlasov Equation},
author = {Antoniazzi, Andrea and Ruffo, Stefano and Califano, Francesco and Fanelli, Duccio and Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL},
abstractNote = {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.},
doi = {10.1103/PHYSREVLETT.98.150602},
journal = {Physical Review Letters},
number = 15,
volume = 98,
place = {United States},
year = {Fri Apr 13 00:00:00 EDT 2007},
month = {Fri Apr 13 00:00:00 EDT 2007}
}