Microscopic Nonreciprocity-Governed Topological Boundary Flows in Active Matter
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=±2 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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BibTeX
@misc{zhu2026microscopic,
title = {{Microscopic Nonreciprocity-Governed Topological Boundary Flows in Active Matter}},
author = {Tong Zhu and Zhigang Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.24926},
eprint = {2606.24926},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.24926},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Microscopic Nonreciprocity-Governed Topological Boundary Flows in Active Matter
AU - Tong Zhu
AU - Zhigang Zheng
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2606.24926
UR - https://arxiv.org/abs/2606.24926
AB - 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=±2 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.
ER -