Discrete spectrum distribution of the Landau Operator Perturbed by an Expanding Electric Potential

2007/11/14 by Grigori Rozenblum, Alexander V. Sobolev, Rozenblum, Grigori +1
Engineering · Mathematics · Physics and Astronomy · #35P20 #47F05 #58J37 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular Junctions and Nanostructures #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory (math.SP) #math-ph #math.MP #math.SP #msc:35P20 #msc:47F05 #msc:58J37

paper · pdf · doi:10.48550/arxiv.0711.2158

22 pages, AMSLaTEX

arxiv created 2007/11/14 · openalex publication_date 2007/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under a perturbation by a decaying electric potential, the Landau Hamiltonian acquires some discrete eigenvalues between the Landau levels. We study the perturbation by an "expanding" electric potential V(t^-1x), t>0, and derive a quasi-classical formula for the counting function of the discrete spectrum as t→ ∞.

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