Bulk topological states in a new collective dynamics model

TL;DR

This paper uncovers topological states in a new collective dynamics model of self-propelled rigid bodies, linking microscopic behavior to macroscopic topological properties and their evolution.

Contribution

It introduces explicit topological solutions in a macroscopic model derived from an individual-based model and analyzes their stability and transition dynamics.

Findings

Explicit topological solutions are identified in the macroscopic model.

The IBM approximates these solutions temporarily before transitioning to trivial states.

Topological indicators reveal the system's transition through maximal disorder.

Abstract

In this paper, we demonstrate the existence of topological states in a new collective dynamics model. This individual-based model (IBM) describes self-propelled rigid bodies moving with constant speed and adjusting their rigid-body attitude to that of their neighbors. In previous works, a macroscopic model has been derived from this IBM in a suitable scaling limit. In the present work, we exhibit explicit solutions of the macroscopic model characterized by a non-trivial topology. We show that these solutions are well approximated by the IBM during a certain time but then the IBM transitions towards topologically trivial states. Using a set of appropriately defined topological indicators, we reveal that the breakage of the non-trivial topology requires the system to go through a phase of maximal disorder. We also show that similar but topologically trivial initial conditions result in markedly different dynamics, suggesting that topology plays a key role in the dynamics of this system.