Eigenfunctions at the threshold energies of magnetic Dirac operators

Abstract

Discussed are $\pm m$ modes and $\pm m$ resonances of Dirac operators with vector potentials $H_A=\alpha \cdot (D-A(x))+m\beta$. Asymptotic limits of $\pm m$ modes at infinity are derived when $|A(x)|\le C<x{>}^{-\rho }$, $\rho >1$, provided that $H_A$ has $\pm m$ modes. In wider classes of vector potentials, sparseness of the vector potentials which give rise to the $\pm m$ modes of $H_A$ are established. It is proved that no $H_A$ has $\pm m$ resonances if $|A(x)|\le C<x{>}^{-\rho }$, $\rho >3/2$.

25 pages, New results are added

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Cited by in corpus (2)

• On Absence of Threshold Resonances for Schrodinger and Dirac Operators
• Spectral theory of first-order systems: from crystals to Dirac operators