Two-dimensional Dirac operators with general δ-shell interactions supported on a straight line

Autor:	Jussi Behrndt, Markus Holzmann, Matěj Tušek
Rok vydání:	2023
Předmět:	Mathematics - Spectral Theory 81Q10 47B93 Statistics and Probability Modeling and Simulation FOS: Mathematics FOS: Physical sciences General Physics and Astronomy Statistical and Nonlinear Physics Mathematical Physics (math-ph) Spectral Theory (math.SP) Mathematical Physics
Zdroj:	Journal of Physics A: Mathematical and Theoretical. 56:045201
ISSN:	1751-8121 1751-8113
Popis:	In this paper the two-dimensional Dirac operator with a general hermitian $\delta$-shell interaction supported on a straight line is introduced as a self-adjoint operator and its spectral properties are investigated in detail. In particular, it is demonstrated that the singularly continuous spectrum is always empty and that by switching a certain $\delta$-shell interaction on, it is possible to generate an eigenvalue in the gap of the spectrum of the free operator or to partially or even fully close the gap. This suggests that the studied operators may serve as interesting continuum toy-models for Dirac materials. Finally, approximations by Dirac operators with regular potentials are presented. Comment: 3 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8375a5ae24009390967d3120db011952 https://doi.org/10.1088/1751-8121/acafaf Zobrazit plný text záznamu