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On absolute continuity of the spectrum of a d-dimensional periodic magnetic Dirac operator

Mathematical Physics 2009-02-19 v3 math.MP Spectral Theory

Abstract

In this paper, for d > 2, we prove the absolute continuity of the spectrum of a d-dimensional periodic Dirac operator with some discontinuous magnetic and electric potentials. In particular, for d = 3, electric potentials from Zygmund classes L3ln1+δL(K)L^3\ln ^{1+\delta}L(K), δ>0\delta >0, and also ones with Coulomb singularities, with constraints on charges depending on the magnetic potential, are admitted (here K is the fundamental domain of the period lattice).

Keywords

Cite

@article{arxiv.0805.0399,
  title  = {On absolute continuity of the spectrum of a d-dimensional periodic magnetic Dirac operator},
  author = {L. I. Danilov},
  journal= {arXiv preprint arXiv:0805.0399},
  year   = {2009}
}

Comments

65 pages, LaTeX. Typos corrected