Microscopic Nonreciprocity-Governed Topological Boundary Flows in Active Matter

Tong Zhu; Zhigang Zheng

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arXiv · 2606.24926

Microscopic Nonreciprocity-Governed Topological Boundary Flows in Active Matter

Tong Zhu·Zhigang Zheng

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Abstract

We connect microscopic nonreciprocity to chiral boundary transport in a minimal frustrated Vicsek--Kuramoto model. Unlike field-level constructions, a low-angular-harmonic closure of particle dynamics yields the non-Hermitian operator. Direction-independent polar projector limits permit wave-number compactification, and the Sakaguchi phase lag reverses the polar spin weights, producing $C=\pm2$ where the closure is nonsingular and the projector remains globally isolated. Strip edge-mode propagation agrees with particle circulation. Crucially, chirality and defect tolerance are distinct: before pattern onset, boundary streams retain chirality on regular convex boundaries but are vulnerable to strong isolated defects; an interior vortex lattice supports a counterpropagating edge stream with substantially stronger defect tolerance in the tested geometries. Thus spectral topology selects a chiral boundary branch, while pattern formation supports its robust nonlinear realization.

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Tong Zhu, Zhigang Zheng. 2026-06-21. Microscopic Nonreciprocity-Governed Topological Boundary Flows in Active Matter. https://arxiv.org/abs/2606.24926

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