Spectral enclosure estimates for non-self-adjoint Dirac operators

We study the spectrum of a periodic non-self-adjoint Dirac operator, and its dependence on a semiclassical parameter is also considered. Several bounds on the spectrum are obtained which provide sharp spectral enclosure estimates. Importantly, a sufficient condition is obtained which ensures semiclassical spectral confinement to the real axis and a bounded subset of the imaginary axis of the spectral plane.