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Effet tunnel pour l’équation de Schrödinger avec champ magnétique. (Tunnel effect for the Schrödinger equation with a magnetic field). (French) Zbl 0699.35205

Les auteurs étudient la spectre “au fond du puits” pour un opérateur de Schrödinger avec champ magnétique sur \({\mathbb{R}}^ n:\) \[ P(h):=\sum^{n}_{j=1}(ih \partial_ j-A_ j)^ 2+V(x). \] Ils mettent l’accent sur les différences avec le cas sans champs magnétique (décroissance des fonctions propres, interactions) et montrent, en particulier, sur des exemples, qu’il peut y avoir diminution de l’effet tunnel entre deux fonds de puits ou bien un phénomène analogue à celui mis en evidence de manière heuristique par Aharonov et Bohm.
Reviewer: J.-C.Nosmas

MSC:

35P99 Spectral theory and eigenvalue problems for partial differential equations
35J10 Schrödinger operator, Schrödinger equation

References:

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