33 citations · 75 across the 13 of their papers we have counts for
13 papers
Relativistic Virial Operators
Lucrezia Cossetti, Luca Fanelli, Fabio Pizzichillo
When studying Dirac operators, it is well known that the phenomenon of Zitterbewegung leads to a lack of convexity of the variance, which creates difficulties in the analysis of di…
A relativistic Hardy-type inequality with minimisers
Luca Fanelli, Fabio Pizzichillo
In this paper, we prove a sharp, weighted Hardy-type inequality for the Dirac operator. A key feature of our result is that the inequality is not only sharp but also attained, and…
Dirac operators with infinite mass boundary conditions on unbounded domains with infinite corners
Miguel Camarasa, Fabio Pizzichillo
We investigate the self-adjointness of the two dimensional Dirac operator with infinite mass boundary conditions on an unbounded domain with an infinite number of corners. We prove…
Keller and Lieb-Thirring estimates of the eigenvalues in the gap of Dirac operators
Jean Dolbeault, David Gontier, Fabio Pizzichillo +1
We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart f…
Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors
Biagio Cassano, Matteo Gallone, Fabio Pizzichillo
We investigate the properties of self-adjointness of a two-dimensional Dirac operator on an infinite sector with infinite mass boundary conditions and in presence of a Coulomb-type…
Dirac operators and shell interactions: a survey
Thomas Ourmières-Bonafos, Fabio Pizzichillo
In this survey we gather recent results on Dirac operators coupled with -shell interactions. We start by discussing recent advances regarding the question of self-adjointness fo…
Self-Adjointness of two dimensional Dirac operators on corner domains
Fabio Pizzichillo, Hanne Van Den Bosch
We investigate the self-adjointness of the two-dimensional Dirac operator , with quantum-dot and Lorentz-scalar -shell boundary conditions, on piecewise domains with fi…
A Hardy-type inequality and some spectral characterizations for the Dirac-Coulomb operator
Biagio Cassano, Fabio Pizzichillo, Luis Vega
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…
Boundary triples for the Dirac operator with Coulomb-type spherically symmetric perturbations
Biagio Cassano, Fabio Pizzichillo
We determine explicitly a boundary triple for the Dirac operator in , for and $\mathbb V(x)= |x|^{-1} ( ν\mathb…
Self-Adjoint Extensions for the Dirac Operator with Coulomb-Type Spherically Symmetric Potentials
Biagio Cassano, Fabio Pizzichillo
We describe the self-adjoint realizations of the operator , for , and $\mathbb V(x)= |x|^{-1} ( ν\mathbb{I}_4 +μβ-i λα\cdot{x…
Spectral asymptotics for -interactions on sharp cones
Thomas Ourmières-Bonafos, Konstantin Pankrashkin, Fabio Pizzichillo
We investigate the spectrum of three-dimensional Schrödinger operators with -interactions of constant strength supported on circular cones. As shown in earlier works, such opera…
The relativistic spherical -shell interaction in : spectrum and approximation
Albert Mas, Fabio Pizzichillo
This note revolves on the free Dirac operator in and its -shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the…
Klein's Paradox and the Relativistic -shell Interaction in
Albert Mas, Fabio Pizzichillo
Under certain hypothesis of smallness of the regular potential , we prove that the Dirac operator in coupled with a suitable re-scaling of c…