Classically Forbidden Regions and Analytic Hypoellipticity in Spectral Theory

Explore the application of analytic microlocal methods in condensed matter physics through this lecture on classically forbidden regions and analytic hypoellipticity. Delve into the structures of eigenstates corresponding to magic angles in twisted graphene sheets, which exhibit superconducting properties. Examine a simple operator believed to determine magical angles, as proposed in a 2019 Physical Review Letter. Learn about the adaptation of analytic hypoellipticity results to demonstrate exponential decay of eigenfunctions in geometrically determined regions as the twisting angle decreases. Discover colorful numerical illustrations suggesting numerous open problems in this field. Gain insights from this joint work with Michael Hitrik, Simon Becker, Mark Embree, and Jens Wittsten, presented as part of the Thematic Programme on "Spectral Theory and Mathematical Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics.