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Self-adjointness of two-dimensional Dirac operators on corner domains
(2021-01-01)
We investigate the self-adjointness of the two-dimensional Dirac operator D, with quantum-dot and Lorentz-scalar i-shell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ...
Dirac Operators and Shell Interactions: A Survey
(2021-01-01)
In this survey we gather recent results on Dirac operators coupled with δ-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterwards we switch to ...
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
(2020-01-01)
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise ...
A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
(2019-07-02)
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise ...
Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
(2018)
We describe the self-adjoint realizations of the operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$, for $m\in\mathbb R $, and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ...
Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$
(2017-11)
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...
Shell interactions for Dirac operators: On the point spectrum and the confinement
(2015-12-31)
Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The ...