Corpus ID: 10109031

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

@article{Danilov2008OnAC,
  title={On absolute continuity of the spectrum of a d-dimensional periodic magnetic Dirac operator},
  author={L. Danilov},
  journal={arXiv: Mathematical Physics},
  year={2008}
}
  • L. Danilov
  • Published 2008
  • Mathematics, Physics
  • arXiv: Mathematical Physics
    • 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 $L^3\ln ^{1+\delta}L(K)$, $\delta >0$, 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). 
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    3 Citations
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    On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator
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    References

    SHOWING 1-10 OF 54 REFERENCES
    On the spectrum of the two-dimensional periodic Dirac operator
    • 9
    The periodic Dirac operator is absolutely continuous
    • 20
    Resolvent estimates and spectrum of the Dirac operator with periodic potential
    • 12
    Absolute Continuity of the Spectra of Two-Dimensional Periodic Magnetic Schrodinger Operator and Dirac Operator with Potentials in the Zygmund Class
    • 6
    Absolute continuity of the spectrum of periodic operators of mathematical physics
    • 23
    • PDF
    Absence of eigenvalues for the generalized two-dimensional periodic Dirac operator
    • 4
    • PDF
    Periodic Magnetic Hamiltonian with a Variable Metric. The Problem of Absolute Continuity
    • 30
    • PDF
    On the structure of spectra of periodic elliptic operators
    • 42
    • PDF
    Uniform Sobolev inequalities and absolute continuity of periodic operators
    • 15
    • Highly Influential
    • PDF
    On Absolute Continuity of the Periodic Schrödinger Operators
    • 39
    • PDF