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Søren Fournais:Tunnelling formulae for magnetic operators

Date: 2025-05-28

Time: 09:15 - 10:15

Zoom link: https://kva-se.zoom.us/j/9217561890

Speaker
Søren Fournais, University of Copenhagen

Abstract

The mathematical analysis of the tunnelling effect between electric wells was a key milestone in semiclassical analysis

reached in the 1980’s with important contributions by Simon and Helffer-Sjöstrand. However, the analysis of the effect

in the presence of magnetic fields was largely left open. Technically, this is because the complex phases that a magnetic

field induces in the eigenfunctions causes cancellations that are delicate to control to the required precision. Although

a general theory of magnetic tunnelling is still lacking at the level of generality of the non-magnetic theory, there has

been important progress in recent years. I will review some recent results, both in very special geometries where separation of variables makes analysis more manageable, and

a recent result which is the first “generic” calculation of a purely magnetic tunnelling effect.

 

Results are in particular in collaboration with Yannick Guedes Bonthonneau, Leo Morin and Nicolas Raymond.