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.
Poisson distribution for gaps between sums of two squares and level spacings for toral point scatterers
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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.