Magnetic Eigenfunctions, Landscapes, and Brownian Motion

In this talk we’ll discuss exponential localization of Schrodinger eigenfunctions in the presence of both scalar and vector potentials (also known as electric and magnetic potentials). After recalling Agmon’s celebrated method of obtaining exponential decay estimates away from the ’classically forbidden region’, and certain approaches to practically determining localized regions via 'landscape functions', we discuss difficulties in this approach in the magnetic case, as well as recent work in the 2d case.