Abstract
We study the dependence of the Laughlin states on the geometry of the sphere and the plane, for one-parameter Mabuchi geodesic families of curved metrics with Hamiltonian \(S^1\)-symmetry. For geodesics associated with convex functions of the symmetry generator, as the geodesic time goes to infinity, the geometry of the sphere becomes that of a thin cigar collapsing to a line and the Laughlin states become concentrated on a discrete set of \(S^1\)-orbits, corresponding to Bohr–Sommerfeld orbits of geometric quantization.
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