General δ-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation

0574839 - ÚJF 2024 RIV DE eng J - Journal Article
Cassano, B. - Lotoreichik, Vladimir - Mas, A. - Tušek, M.
General δ-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation.
Revista Matematica Iberoamericana. Roč. 39, č. 4 (2023), s. 1443-1492. ISSN 0213-2230
R&D Projects: GA ČR(CZ) GA21-07129S
Institutional support: RVO:61389005
Keywords : Dirac operator * quantum-dot * Lorentz-scalar 8-shell * boundary conditions * self-adjoint operator * conformal map
OECD category: Pure mathematics
Impact factor: 1.2, year: 2022
Method of publishing: Open access
https://doi.org/10.4171/rmi/1354

In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator. In the non-critical case, we do so by providing a boundary triple, and in the critical purely magnetic case, by exploiting the phenomenon of confinement and super-symmetry. Moreover, we justify our model by showing that Dirac operators with singular interactions are limits in the strong resolvent sense of Dirac operators with regular potentials.
Permanent Link: https://hdl.handle.net/11104/0344774