Propriétés spectrales de l'opérateur de Dirac avec un champ magnétique intense

Abstract : We study bidimensional Dirac operator with magnetic fields which grow unboundedly at infinity. The spectrum of such operator is composed only of eigenvalues and in particular the essential spectrum is reduced to one point. For power-like increasing magnetic field, we give an equivalent of the eigenvalues at infinity.
When we perturbe this operator by an electric potential which decays to zero at infinity with power-like decay, exponential decay or with compact support, some eigenvalues are created near essential spectrum. We investigate the asymptotic behaviour of the discrete spectrum near this point.
For tridimensional Dirac operator with constant magnetic fields, we define resonances with analytical dilatation. Using Grushin's method, we study the resonances near Landau-Dirac levels with the help of effective hamiltonian.
Document type :
Mathématiques [math]. Université de Nantes, 2006. Français
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Arnaud Sourisse. Propriétés spectrales de l'opérateur de Dirac avec un champ magnétique intense. Mathématiques [math]. Université de Nantes, 2006. Français. 〈tel-00088078〉



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