Velocity and Speed Correlations in Hamiltonian Flocks

TL;DR

This paper investigates a 2D Hamiltonian fluid with spin-coupled particles, revealing phase coexistence, flock-like correlations, and the role of angular momentum in shape and correlation scaling.

Contribution

It introduces a Hamiltonian model exhibiting flock-like behavior and analyzes how angular momentum conservation influences correlations and shape dynamics.

Findings

Phase coexistence between a moving droplet and a gas.

Flock-like correlations in particle displacements.

Rigid rotations driven by angular momentum conservation.

Abstract

We study a $2d$ Hamiltonian fluid made of particles carrying spins coupled to their velocities. At low temperatures and intermediate densities, this conservative system exhibits phase coexistence between a collectively moving droplet and a still gas. The particle displacements within the droplet have remarkably similar correlations to those of birds flocks. The center of mass behaves as an effective self-propelled particle, driven by the droplet's total magnetization. The conservation of a generalized angular momentum leads to rigid rotations, opposite to the fluctuations of the magnetization orientation that, however small, are responsible for the shape and scaling of the correlations.