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PreprintCC BY 4.0arXiv

Topology of Fluctuation Bands in Chiral Active Crystals

  • Raphaël Maire
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Abstract

While band topology is usually associated with the deterministic dynamics of a system, we show that it can instead reside in its fluctuations. Using a reciprocal lattice driven by nonequilibrium chiral active noise, we find that the displacement spectrum---which quantifies displacement fluctuations---admits bands with nonzero Chern numbers despite a Chern-trivial deterministic mechanics. A two-band valley theory captures the emergence of this topology through a Dirac mass inversion, a Haldane-type mechanism, or a quadratic band touching, depending on the relevant transition. Through the bulk--boundary correspondence, we find boundary-localized fluctuation modes that are distinct from the usual propagating mechanical edge states.

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Cite

BibTeXRIS
BibTeX
@misc{maire2026topology,
  title = {{Topology of Fluctuation Bands in Chiral Active Crystals}},
  author = {Raphaël Maire},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.26055},
  eprint = {2608.26055},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.26055},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Topology of Fluctuation Bands in Chiral Active Crystals
AU  - Raphaël Maire
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2608.26055
UR  - https://arxiv.org/abs/2608.26055
AB  - While band topology is usually associated with the deterministic dynamics of a system, we show that it can instead reside in its fluctuations. Using a reciprocal lattice driven by nonequilibrium chiral active noise, we find that the displacement spectrum---which quantifies displacement fluctuations---admits bands with nonzero Chern numbers despite a Chern-trivial deterministic mechanics. A two-band valley theory captures the emergence of this topology through a Dirac mass inversion, a Haldane-type mechanism, or a quadratic band touching, depending on the relevant transition. Through the bulk--boundary correspondence, we find boundary-localized fluctuation modes that are distinct from the usual propagating mechanical edge states.
ER  -