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Magnetic WKB constructions

Nicolas Raymond
(Universite de Rennes)
Tirsdag, 7 oktober, 2014, at 16:15-17:00, in Koll. G4 (1532-222)

This talk will be devoted to the semiclassical magnetic Laplacian. Until now WKB expansions for the eigenfunctions were only established in presence of a non-zero electric potential. In this talk we will tackle the pure magnetic case. Thanks to Feynman-Hellmann type formulas and a coherent states decomposition, we will present a magnetic Born-Oppenheimer theory. Exploiting the multiple scales of the problem, we will explain how we can solve an effective eikonal equation in pure magnetic cases and obtain WKB expansions. We will also investigate explicit examples for which we can improve our general theorem: global WKB expansions, quasi-optimal estimates of Agmon and upper bound of the tunelling effect (in symmetric cases). We will also apply our strategy to get more accurate descriptions of the eigenfunctions in a wide range of situations analyzed in the last two decades.

This is joint work with V. Bonnaillie-Noël and F. Hérau.

Kontaktperson: Søren Fournais