Browsing by Author "Pizzichillo, F."
Now showing items 1-11 of 11
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Boundary Triples for the Dirac Operator with Coulomb-Type Spherically Symmetric Perturbations
(2019-02)We determine explicitly a boundary triple for the Dirac operator $H:=-i\alpha\cdot \nabla + m\beta + \mathbb V(x)$ in $\mathbb R^3$, for $m\in\mathbb R$ and $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda ... -
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
Cassano, B.; Pizzichillo, F.; Vega, L.
(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 ... -
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
Cassano, B.; Pizzichillo, F.; Vega, L. (2019-06)
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 $\mathbf V$ of Coulomb type: ... -
A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
Cassano, B.; Pizzichillo, F.; Vega, L. (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 ... -
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 ... -
The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
(2017-08-03)This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ... -
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 $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ... -
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 ... -
Singular Perturbation of the Dirac Hamiltonian
(2017-12-15)This thesis is devoted to the study of the Dirac Hamiltonian perturbed by delta-type potentials and Coulomb-type potentials. We analysed the delta-shell interaction on bounded and smooth domains and its approximation by ... -
Spectral asymptotics for $\delta$-interactions on sharp cones
(2017)We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...