Bulk topological states in a new collective dynamics model

Pierre Degond; Antoine Diez; Mingye Na

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arXiv · 2101.10864

Bulk topological states in a new collective dynamics model

Pierre Degond·Antoine Diez·Mingye Na

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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.

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Pierre Degond, Antoine Diez, Mingye Na. 2021-01-22. Bulk topological states in a new collective dynamics model. https://arxiv.org/abs/2101.10864

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