Collective motion in a Hamiltonian dynamical system

TL;DR

This paper investigates long-lasting collective oscillations in a Hamiltonian mean field XY model, revealing a Hopf bifurcation as the mechanism and discussing the universality of these phenomena.

Contribution

It demonstrates the emergence of collective oscillations via Hopf bifurcation in a Hamiltonian system, a phenomenon typically associated with dissipative systems.

Findings

Oscillations last longer with increasing system size.

Oscillations originate from self-excited swings in the mean field.

Universality of the phenomenon is discussed.

Abstract

Oscillation of macroscopic variables is discovered in a metastable state in the Hamiltonian dynamical system of mean field XY model, the duration of which is divergent with the system size. This long-lasting periodic or quasiperiodic collective motion appears through Hopf bifurcation, which is a typical route in low-dimensional dissipative dynamical systems. The origin of the oscillation is explained, with self-consistent analysis of the distribution function, as the emergence of self-excited ``swings'' through the mean-field. The universality of the phenomena is also discussed.