Velocity and Speed Correlations in Hamiltonian Flocks

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.

arXiv commentMain text: 6 pages, 4 figures. Supplementary Information: 13 pages, 5 figures, 2 movies

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• Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking
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• A geometric condition for robot-swarm cohesion and cluster-flock transition
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• The BKT Transition and its Dynamics in a Spin Fluid
• Boundary-induced classical Generalized Gibbs Ensemble with angular momentum