07-133 Takuya Mine, Yuji Nomura

The spectrum of Schr\"odinger operators with random \delta magnetic fields (97K, Latex2e) May 30, 07

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Abstract. We shall consider the Schr\"odinger operators on $\mathbf{R}^2$ with the magnetic field given by a nonnegative constant field plus random $\delta$ 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 using the entire function theory by Levin.

Files: 07-133.src( mine_nomura.tex , 07-133.keywords.mm )