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The spectrum of Schrödinger operators with random $δ$ magnetic fields

Takuya Mine; Yuji Nomura — 2009

Annales de l’institut Fourier

We shall consider the Schrödinger operators on $ℝ^{2}$ with the magnetic field given by a nonnegative constant field plus random $δ$ magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...

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The spectrum of Schrödinger operators with random δ magnetic fields

The spectrum of Schrödinger operators with random $δ$ magnetic fields