A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian

Details A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian

2003-10-02

arxiv.org/abs/math/0310021v1

Mathematics

Spectral Theory

23 pages

Scientific paper

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.

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