The fate of Landau levels under -interactions

  • Jussi Behrndt

    Technische Universität Graz, Austria
  • Markus Holzmann

    Technische Universität Graz, Austria
  • Vladimir Lotoreichik

    Nuclear Physics Institute, Řež - Prague, Czechia
  • Georgi Raikov

    Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
The fate of Landau levels under  $\delta$-interactions cover
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We consider the self-adjoint Landau Hamiltonian in whose spectrum consists of infinitely degenerate eigenvalues , , and the perturbed Landau Hamiltonian , where is a regular Jordan -curve and , , has a constant sign. We investigate , , and show that generically

where , is an operator of Berezin–Toeplitz type, acting in , and is the orthogonal projection onto . If and , then we prove that . If and is a circle of radius , then we show that , and the set of for which is infinite and discrete.

Cite this article

Jussi Behrndt, Markus Holzmann, Vladimir Lotoreichik, Georgi Raikov, The fate of Landau levels under -interactions. J. Spectr. Theory 12 (2022), no. 3, pp. 1203–1234

DOI 10.4171/JST/422