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

Grigori Rozenblum; Alexander V. Sobolev

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arXiv · 0711.2158

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

Grigori Rozenblum·Alexander V. Sobolev

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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 $V(t^{-1}x)$, $t>0$, and derive a quasi-classical formula for the counting function of the discrete spectrum as $t\to \infty$.

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BibTeX RIS

Grigori Rozenblum, Alexander V. Sobolev. 2007-11-14. Discrete spectrum distribution of the Landau Operator Perturbed by an Expanding Electric Potential. https://arxiv.org/abs/0711.2158

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