Publications

Scaling asymptotics for ladder sequences of spherical harmonics at caustic latitudes

We prove that certain ‘ladder’ sequences of spherical harmonics are Lagrangian distributions whose semi-classical $L^2$ mass lies over a band around the standard equator of $S^2$ bounded by latitude circles which are caustics. We derive Airy scaling asymptotics for such sequences in a shrinking neighborhood of these caustic latitudes.

Scaling Asymptotics for Ladder Sequences of Spherical Harmonics at Caustic Latitudes, Pre-print, arXiv:2208.02770”

Concentration of quantum integrable eigenfunctions on a convex surface of revolution

We compute weak-$*$ limits of normalized empirical measures of joint eigenfunctions of the Laplacian and the generator of the $S^1$ symmetry on a convex surface of revolution. These measures detect the relative amounts of $L^2$ mass concentration of mass of the eigenfunctions restricted to the unique $S^1$ invariant geodesic, $H$.

Concentration of Quantum Integrable Eigenfunctions on a Convex Surface of Revolution, arXiv: 2008.12482, submitted for review, Journal of Spectral Theory.