Non-self-adjoint Dirac operators on graphs
Mathematical Physics
2025-04-09 v2 math.MP
Spectral Theory
Quantum Physics
Abstract
In this paper we introduce and study generally non-self-adjoint realizations of the Dirac operator on an arbitrary finite metric graph. Employing the robust boundary triple framework, we derive, in particular, a variant of the Birman Schwinger principle for its eigenvalues, and with an example of a star shaped graph we show that the point spectrum may exhibit diverse behaviour. Subsequently, we find sufficient and necessary conditions on transmission conditions at the graph's vertices under which the Dirac operator on the graph is symmetric with respect to the parity, the time reversal, or the charge conjugation transformation.
Keywords
Cite
@article{arxiv.2502.00480,
title = {Non-self-adjoint Dirac operators on graphs},
author = {Markus Holzmann and Václav Růžek and Matěj Tušek},
journal= {arXiv preprint arXiv:2502.00480},
year = {2025}
}