A singular delta potential supported on an equator of S^2 permits sequences of eigenfunctions whose semiclassical measures are not invariant under geodesic flow, with asymptotic concentration on one hemisphere.
Quantum chaos for point scatterers on flat tori
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Quantum Limits of the Laplacian perturbed along a geodesic on $\mathbb{S}^{2}$
A singular delta potential supported on an equator of S^2 permits sequences of eigenfunctions whose semiclassical measures are not invariant under geodesic flow, with asymptotic concentration on one hemisphere.