Location of eigenvalues of non-self-adjoint discrete Dirac operators

Abstract

We provide quantitative estimates on the location of eigenvalues of one-dimensional discrete Dirac operators with complex ${\ell }^p$-potentials for $1\le p\le \infty$. As a corollary, subsets of the essential spectrum free of embedded eigenvalues are determined for small ${\ell }^1$-potential. Further possible improvements and sharpness of the obtained spectral bounds are also discussed.

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• Continuum limits for discrete Dirac operators on 2D square lattices
• The relativistic rotated harmonic oscillator