2003/10/02 by Evgeni Korotyaev, Korotyaev, Evgeni, Alexander Pushnitski +1
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP
paper · pdf · doi:10.48550/arxiv.math/0310021
23 pages
arxiv created 2003/10/02 · openalex publication_date 2003/10/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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→∞. 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.