03-450 Evgeni Korotyaev, Alexander Pushnitski

A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian (71K, Latex2e) Oct 2, 03

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Abstract. A two-dimensional 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: 03-450.src( 03-450.keywords , landau_preprint.tex )