Evgeni Korotyaev, Alexander Pushnitski
A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian
(71K, Latex2e)
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.