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

2012/07/15 by Sylvain Golénia, Golenia, Sylvain, Tristan Haugomat +1 · 2 citations
Computer Science · Mathematics · #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1207.3516

openalex publication_date 2012/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Principles of Quantum Mechanics

Cited by

• On the spectral properties of long-range perturbations of a class of block finite difference operators
• Interior Spectral Windows and Transport for Discrete Fractional Laplacians on d-Dimensional Hypercubic Lattices

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