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

Evgeni Korotyaev; Alexander Pushnitski

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arXiv · math/0310021

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

Evgeni Korotyaev·Alexander Pushnitski

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Abstract

A two-dimensional Schrödinger 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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BibTeX RIS

Evgeni Korotyaev, Alexander Pushnitski. 2003-10-02. A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian. https://arxiv.org/abs/math/0310021

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