Polar active liquids: a universal classification rooted in nonconservation of momentum

TL;DR

This paper develops a universal classification for polar active liquids based on the nonconservation of momentum, analyzing phase transitions from isotropic to collective motion using Boltzmann formalism.

Contribution

It introduces a novel criterion for phase stability in polar active particles, linking momentum change to transition nature, validated by numerical simulations.

Findings

The criterion accurately predicts phase transition types.

The approach applies to multiple classes of models.

Theoretical results match numerical simulations.

Abstract

We study the spatially homogeneous phases of polar active particles in the low density limit, and specifically the transition from the isotropic phase to collective polar motion. We show that the fundamental quantity of interest for the stability of the isotropic phase is the forward component of the momentum change induced by binary scattering events. Building on the Boltzmann formalism, we introduce an ansatz for the one-particle distribution and derive a closed-form evolution equation for the order parameter. This approach yields a very intuitive and physically meaningful criterion for the destabilization of the isotropic phase, where the ansatz is exact. The criterion also predicts whether the transition is continuous or discontinuous, as illustrated in three different classes of models. The theoretical predictions are in excellent agreement with numerical results.