Bernard Helffer: Mini course on Semi-classical approximation and the tunnelling effect

Tid: Ti 2019-01-29 kl 09.00 - 11.00

Föreläsare: Bernard Helffer, Université de Nantes

Plats: Seminar Hall Kuskvillan, Institut Mittag-Leffler

In 1982-1983, the so-called symmetric double well problem was rigorously analyzed in any dimension in the semi-classical context by B. Agmon (announced in 1982) and Helffer-Sjöstrand (1983). This involves semi-classical Agmon estimates, WKB constructions and a very fine analysis of the so-called tunneling effect in order to establish the splitting between the lowest eigenvalues.

The strategy followed by Helffer-Sjöstrand appears to be quite efficient in many other contexts. We will focus on the Robin problem for the Laplacian in a domain where in some asymptotic regime for the Robin parameter and some specific symmetric domain (ellipse like domain) a double well appears.
We will also discuss the case of the magnetic Laplacian with large constant magnetic field in a similar domain. The optimal result in this case is still open.

The results correspond to contributions by various subsets of the following set of authors : Bonnaillie, Fournais, Helffer, Hérau, Kachmar, Morame, Pankrashkin, Popoff, Raymond, Sjöstrand.