Topology of Fluctuation Bands in Chiral Active Matter

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 Haldane-like effective coupling in the correlation spectrum explains this topology and produces topological transitions controlled by both the stochastic driving and the observation frequency. Through the bulk--boundary correspondence, we find boundary-localized fluctuation modes that are distinct from the usual propagating mechanical edge states.