55 research outputs found
Schnol's theorem and spectral properties of massless Dirac operators with scalar potentials
The spectra of massless Dirac operators are of essential interest e.g. for
the electronic properties of graphene, but fundamental questions such as the
existence of spectral gaps remain open. We show that the eigenvalues of
massless Dirac operators with suitable real-valued potentials lie inside small
sets easily characterised in terms of properties of the potentials, and we
prove a Schnol'-type theorem relating spectral points to polynomial boundedness
of solutions of the Dirac equation. Moreover, we show that, under minimal
hypotheses which leave the potential essentially unrestrained in large parts of
space, the spectrum of the massless Dirac operator covers the whole real line;
in particular, this will be the case if the potential is nearly constant in a
sequence of regions.Comment: 18 page
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