 03450 Evgeni Korotyaev, Alexander Pushnitski
 A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian
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Oct 2, 03

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Abstract. A twodimensional Schr\"odinger operator with a constant
magnetic field perturbed by a smooth compactly supported potential
is considered. The spectrum of this operator consists of
eigenvalues which accumulate to the Landau levels.
We call the set of eigenvalues near the $n$'th Landau level
an $n$'th eigenvalue cluster, and study the distribution of
eigenvalues in the $n$'th cluster as $n\to\infty$.
A complete asymptotic expansion for the eigenvalue moments
in the $n$'th cluster is obtained and some coefficients
of this expansion are computed. A trace formula involving the
first eigenvalue moments is obtained.
 Files:
03450.src(
03450.keywords ,
landau_preprint.tex )