Eigenfunctions at the threshold energies of magnetic Dirac operators

Details Eigenfunctions at the threshold energies of magnetic Dirac operators Eigenfunctions at the threshold energies of magnetic Dirac operators

2009-05-07

arxiv.org/abs/0905.0961v3

Mathematics

Spectral Theory

25 pages, New results are added

Scientific paper

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 $|A(x)| \le C^{-\rho}$, $\rho > 1$, 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 $|A(x)|\le C^{-\rho}$, $\rho >3/2$.

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