Naiara Arrizabalaga

activity

20112025

most citedOn the MIT bag model: self-adjointness and non-relativistic limit

46 citations · 134 across the 9 of their papers we have counts for

collaborators

11 papers

math.SP2025

On the point spectrum of electromagnetic Dirac operators

Naiara Arrizabalaga, Lucrezia Cossetti, Matias Morales

In this work, we develop the method of multipliers for electromagnetic Dirac operators and establish sufficient conditions on the magnetic and electric fields that guarantee the ab…

math.AP2021★ 9 cited

Eigenvalue curves for generalized MIT bag models

Naiara Arrizabalaga, Albert Mas, Tomás Sanz-Perela +1

We study spectral properties of Dirac operators on bounded domains $Ω \subset R^{3}$ with boundary conditions of electrostatic and Lorentz scalar type and which depend on a p…

math.AP2018

The MIT Bag Model as an infinite mass limit

Naiara Arrizabalaga, Loïc Le Treust, Albert Mas +1

The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass $m > 0$ lies outside a smooth and bounded open set $Ω \subset R^{3}$ , it is proved that its spe…

math.SP2016★ 46 cited

On the MIT bag model: self-adjointness and non-relativistic limit

Naiara Arrizabalaga, Loïc Le Treust, Nicolas Raymond

This paper is devoted to the mathematical investigation of the MIT bag model, that is the Dirac operator on a smooth and bounded domain with certain boundary conditions. We prove t…

math-ph2015★ 26 cited

An isoperimetric-type inequality for electrostatic shell interactions for Dirac operators

Naiara Arrizabalaga, Albert Mas, Luis Vega

In this article we investigate spectral properties of the coupling $H + V_{λ}$ , where $H = - i α \cdot \nabla + m β$ is the free Dirac operator in $R^{3}$ , $m > 0$ and $V_{λ}$ is an electros…

math.AP2014

Shell interactions for Dirac operators: on the point spectrum and the confinement

Naiara Arrizabalaga, Albert Mas, Luis Vega

Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H = - i α \cdot \nabla + m β$ is the free Dirac operator in $R^{3}$ and $V$ is a measu…

math.AP2013

Unique continuation for magnetic Schrödinger operator with singular potentials

Naiara Arrizabalaga, Miren Zubeldia

In this paper we study unique continuation theorems for magnetic Schrödinger equation via Carleman estimates. We use integration by parts techniques in order to show these estimate…

math.AP2013

Shell interactions for Dirac operators

Naiara Arrizabalaga, Albert Mas, Luis Vega

The self-adjointness of $H + V$ is studied, where $H = - i α \cdot \nabla + m β$ is the free Dirac operator in $R^{3}$ and $V$ is a measure-valued potential. The potentials $V$ under consider…

math.AP2012★ 33 cited

Self-adjoint extensions of Dirac operators with Coulomb type singularity

Naiara Arrizabalaga, Javier Duoandikoetxea, Luis Vega

In this work we construct self-adjoint extensions of the Dirac operator associated to Hermitian matrix potentials with Coulomb decay and prove that the domain is maximal. The resul…

math.AP2011

On the lack of dispersion for a class of magnetic Dirac flows

Naiara Arrizabalaga, Luca Fanelli, Andoni García

We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at infinity. In order to prove this, we construct…

math.AP2011★ 20 cited

Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities

Naiara Arrizabalaga

We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint e…