On the a.c. spectrum of the 1D discrete Dirac operator. (English) Zbl 1324.47066

The authors study perturbations of electrical type of the discrete Dirac operator. Under certain conditions, they prove that such operators have purely absolutely continuous spectrum. More general cases of mixtures of magnetic and Witten-type perturbations, as well as the operators on \(\mathbb Z_+\), are also considered. As the authors say, they “reduce the problem to a nonselfadjoint Laplacian-like operator by using a spin up/down decomposition and rely on a transfer matrices technique”.


47B39 Linear difference operators
39A70 Difference operators
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
Full Text: arXiv