Flocks on a Sphere Sound Topological!
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Flocking, the self-organized and spontaneous motion of a large collection of self-propelled entities, is ubiquitous in the natural world. Such collective motion, for instance in groups of cells advancing en masse during growth and development, often happens on curved surfaces. Curvature frustrates orientational order and leads to inhomogeneous steady states, possibly with defects. Additionally, curvature also generates a gap in the spectrum of long-wavelength sound modes that are present in an ordered polar flock. The breaking of time reversal symmetry due to spontaneous flow and the presence of a spectral gap leads to topologically protected sound modes that propagate unidirectionally and are localized to special geodesics on the surface, like the equator on a sphere. Analogous to edge states in quantum Hall systems or well-known equatorial waves in atmospheric flows, these modes can provide robust channels for information transport in the flock immune to disorder and backscattering.
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