Semiclassical methods and tunneling effects: old and new
Bernard Helffer (Paris-Sud / Nantes)
Abstract: In 1982-1983 the so-called symmetric double well problem was rigorously analyzed in any dimension in the semi-classical context by B. Simon and Helffer-Sjöstrand. This involves semi-classical Agmon estimates, Harmonic approximation, 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. After recalling how it works on the initial double well problem, we will discuss in a rather impressionist way the main successes of the approach along the years. Finally we will focus on a quite recent result by Bonnaillie-Hérau-Raymond devoted to the measure of a magnetic tunneling in Surface Superconductivity and discuss open problems.
The presented results correspond to contributions by various subsets of the following set of authors : Bonnaillie, Fournais, Helffer, Hérau, Kachmar, Morame, Nier, Raymond, Simon, Sjöstrand and many others...
mathematical physics
Audience: researchers in the discipline
( video )
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Organizers: | Margherita Disertori*, Wojciech Dybalski*, Ian Jauslin, Hal Tasaki* |
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