Raphaël MAIRE : Topology from Noise in Chiral Active Matter

In classical systems, topology is typically associated with the deterministic dynamics of a system. Topological waves in fluids or metamaterials, for instance, arise from deterministic time evolution, with fluctuations playing only a secondary role. In this talk, however, we will show that observables related to fluctuations can carry a nontrivial band topology, even when both the deterministic dynamics and the fluctuating forcing are Chern-trivial.

We take chiral active particles on a lattice as an example and study their displacement spectrum. We find that this spectrum has topologically nontrivial bands due to a mechanism reminiscent of the one underlying topology in Haldane’s model. We then show how this topology leads to the robust localization of fluctuation modes at boundaries.

Paper: https://arxiv.org/abs/2608.26055