Hard-core collisional dynamics in Hamiltonian mean-field model

• Published in: Communications in nonlinear science & numerical simulation Vol. 87; p. 105270
• Main Authors: Melo, I., Figueiredo, A., Rocha Filho, T.M., Miranda Filho, L.H., Elskens, Y.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2020; Elsevier Science Ltd; Elsevier
• Subjects: Chaotic Dynamics; Condensed Matter; Critical temperature; Fluid mechanics; Long-range interactions; Many-particle systems; Nonlinear Sciences; Numerical analysis; Numerical integration; Phase transitions; Physics; Plasma Physics; Statistical Mechanics; Temperature; Violent relaxation; Violent relaxation; Many-particle systems; Long-range interactions; event-driven; long-range systems; collisional HMF model
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2020.105270

•Systems with long range interactions have drawn a great deal of attention over the last few decades, not only because they are common in nature (e.g. self-gravitating systems and charged plasmas), but also due to many unusual phenomena not observed in short-range interacting systems. In the present paper we discuss for the Hamiltonian mean-field model, a much studied system, the effects on the system dynamics of the introduction of a hard-core point-like interaction, resulting in a system with both global and strong short-range interactions.•We developed a numeric algorithm for the molecular dynamics of this type of mixed interaction, and applied it to understand how the violent relaxation and the long-term dynamics are altered.•This is a first and original step to understand how the special phenomenology of long-range interacting systems is altered by hard-core potentials, and point to new research and relevant open problems. We consider a modification of the well studied Hamiltonian Mean-Field model with cosine potential by introducing a hard-core point-like repulsive interaction and propose a numerical integration scheme to integrate its dynamics. Our results show that the outcome of the initial violent relaxation is altered, and also that the phase-diagram is modified with a critical temperature at a higher value than in its counterpart without hard-core collisions.