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Self-adjointness of two-dimensional Dirac operators on corner domains 

Pizzichillo, F.; Van Den Bosch, H. (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 ...
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Dirac Operators and Shell Interactions: A Survey 

Ourmières-Bonafos, T.; Pizzichillo, F. (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 ...
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A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator 

Cassano, B.; Pizzichillo, F.; Vega, L.Autoridad BCAM (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 ...
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A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator 

Cassano, B.; Pizzichillo, F.; Vega, L.Autoridad BCAM (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 ...
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A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator 

Cassano, B.; Pizzichillo, F.; Vega, L.Autoridad BCAM (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: ...
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Boundary Triples for the Dirac Operator with Coulomb-Type Spherically Symmetric Perturbations 

Cassano, B.; Pizzichillo, F. (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 ...
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Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials 

Cassano, B.; Pizzichillo, F. (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 $\mathbb V(x)= |x|^{-1} ( \nu \mathbb{I}_4 +\mu \beta -i \lambda \alpha\cdot{x}/{|x|}\,\beta)$, ...
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Singular Perturbation of the Dirac Hamiltonian 

Pizzichillo, F. (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 ...
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Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ 

Mas, A.; Pizzichillo, F. (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 ...
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The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation 

Mas, A.; Pizzichillo, F. (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 ...
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Pizzichillo, F. (11)
Cassano, B. (5)Vega, L. (3)Mas, A. (2)Ourmières-Bonafos, T. (2)Pankrashkin, K. (1)Van Den Bosch, H. (1)SubjectDirac operator (6)Coulomb potential (3)Hardy inequality (3)Self-adjoint operator (2)self-adjoint operator (2)$\delta$-interaction (1)$\delta$-shell interaction (1)approximation by scaled regular potentials (1)asymptotic analysis (1)Boundary conditions (1)... másFecha2021 (2)2020 (1)2019 (3)2018 (1)2017 (4)

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