On the a.c. spectrum of 1D discrete Dirac operator

Abstract

In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint Laplacian-like operator by using a spin up/down decomposition and rely on a transfermatrices technique.

Small changes. The article will be published in Methods of Functional Analysis and Topology

References in corpus (2)

• Limiting absorption principle for some long range perturbations of Dirac systems at threshold energies
• Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator

Cited by in corpus (3)

• Location of eigenvalues of non-self-adjoint discrete Dirac operators
• One-dimensional Discrete Dirac Operators in a Decaying Random Potential I: Spectrum and Dynamics
• Spectral and scattering theory for Gauss-Bonnet operators on perturbed topological crystals