QLunch: Léo Morin

Speaker: Léo Morin

Title: A purely magnetic tunneling formula between 2D magnetic wells

Abstract: Tunneling is a well-known phenomenon in quantum physics: A charged particle in symmetric double-well electric potential is localized in both wells simultaneously. A way to quantify this phenomenon is by estimating the spectral gap between the first two eigenvalues of the corresponding Schrödinger operator. In the semiclassical limit, this gap is exponentially small. Such sharp estimates were obtained by Helffer-Sjöstrand in the 80’s. When the localization is induced by a magnetic field instead, without electric potential, a similar effect was conjectured by Helffer-Morame in 1996. However, the magnetic case turned out to be more complicated to understand. After recent partial results, we finally proved such a tunneling formula between purely magnetic wells, hence answering a 30 years old problem. Interestingly, the size of the interaction is smaller than the one conjectured in 1996.