Eigenvalue bounds for perturbed periodic Dirac operators
Year: 2025
Type: article
Abstract: We characterise regions in the complex plane that contain all non-embedded eigenvalues of a perturbed periodic Dirac operator on the real line with real-valued periodic potential and a generally non-symmetric matrix-valued perturbation V . We show that the eigenvalues are located close to the end-points of the spectral bands for small V\in L^{1}(\mathbb{R})^{2\times 2} , but only close to the spectral bands as a whole for small V\in L^{p}(\mathbb{R})^{2\times 2} , p > 1 . As auxiliary results, we prove the relative compactness of matrix multiplication operators in L^{2p}(\mathbb{R})^{2\times 2} with respect to the periodic operator under minimal hypotheses, and find the asymptotic solution of the Dirac equation on a finite interval for spectral parameters with large imaginary part.
Source: Journal of Spectral Theory
DOI: 10.4171/jst/556
Authors: Ghada Shuker Jameel, Karl Michael Schmidt
Institutions: University of Mosul, Cardiff University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: University of Mosul
OpenAlex ID: W4410779846