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

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

2007-11-14

arxiv.org/abs/0711.2158v1

Mathematics

Spectral Theory

22 pages, AMSLaTEX

Scientific paper

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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