Spectral Properties of 2D Pauli Operators with Almost-Periodic Electromagnetic Fields

  • Jean-François Bony

    Université de Bordeaux, Talence, France
  • Nicolás Espinoza

    University of Tokyo, Japan
  • Georgi Raikov

    Pontificia Universidad Católica de Chile, Santiago, Chile
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Abstract

We consider a 2D Pauli operator with almost-periodic field and electric potential . First, we study the ergodic properties of and show, in particular, that its discrete spectrum is empty if there exists a magnetic potential which generates the magnetic field , where is the mean value of . Next, we assume that , and investigate the zero modes of . As expected, if , then generically dim Ker . If , then for each , we construct an almost-periodic such that dim Ker . This construction depends strongly on results concerning the asymptotic behavior of Dirichlet series, also obtained in the present article.

Cite this article

Jean-François Bony, Nicolás Espinoza, Georgi Raikov, Spectral Properties of 2D Pauli Operators with Almost-Periodic Electromagnetic Fields. Publ. Res. Inst. Math. Sci. 55 (2019), no. 3, pp. 453–487

DOI 10.4171/PRIMS/55-3-1