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

Sylvain Golenia (1) , Tristan Haugomat (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 ENS Cachan Bretagne - École normale supérieure - Cachan, antenne de Bretagne

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.

Mots clés: discrete Dirac; ac spectrum; 1-dimensional; jacobi matrix

Domaines: Physique mathématique [math-ph]; Théorie spectrale [math.SP]; Analyse fonctionnelle [math.FA]

Sylvain Golenia, Tristan Haugomat. On the a.c. spectrum of 1D discrete Dirac operator. 2014. ⟨hal-00717811v2⟩