Related papers: Dirac operators and shell interactions: a survey
This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions…
In this paper we study the self-adjointness and spectral properties of two-dimensional Dirac operators with electrostatic, Lorentz scalar, and anomalous magnetic $\delta$-shell interactions with constant weights that are supported on a…
In this article Dirac operators $A_{\eta, \tau}$ coupled with combinations of electrostatic and Lorentz scalar $\delta$-shell interactions of constant strength $\eta$ and $\tau$, respectively, supported on compact surfaces $\Sigma \subset…
In this paper we study the approximation of Dirac operators with $\delta$-shell potentials in the norm resolvent sense. In particular, we consider the approximation of Dirac operators with confining electrostatic and Lorentz scalar…
In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four…
We consider the three-dimensional Dirac operator coupled with a combination of electrostatic and Lorentz scalar $\delta$-shell interactions. We approximate this operator with general local interactions $V$. Without any hypotheses of…
In this paper the spectral properties of Dirac operators $A_\eta$ with electrostatic $\delta$-shell interactions of constant strength $\eta$ supported on compact smooth surfaces in $\mathbb{R}^3$ are studied. Making use of boundary triple…
In this paper the approximation of Dirac operators with general $\delta$-shell potentials supported on $C^2$-curves in $\mathbb{R}^2$ or $C^2$-surfaces in $\mathbb{R}^3$, which may be bounded or unbounded, is studied. It is shown under…
In this paper the two-dimensional Dirac operator with a general hermitian $\delta$-shell interaction supported on a straight line is introduced as a self-adjoint operator and its spectral properties are investigated in detail. In…
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 finding sharp…
We provide a limiting absorption principle for self-adjoint realizations of Dirac operators with electrostatic and Lorentz scalar $\delta$-shell interactions supported on regular compact surfaces. Then we show completeness of the wave…
This paper is devoted to the approximation of two and three-dimensional Dirac operators $H_{\widetilde{V} \delta_\Sigma}$ with combinations of electrostatic and Lorentz scalar $\delta$-shell interactions in the norm resolvent sense. Relying…
In this paper, new self-adjoint realizations of the Dirac operator in dimension two and three are introduced. It is shown that they may be associated with the formal expression $\mathcal{D}_0+|F\delta_\Sigma\rangle\langle G\delta_\Sigma|$,…
Let $\Omega\subset\mathbb{R}^3$ be an open set, we study the spectral properties of the free Dirac operator $\mathcal{H}$ coupled with the singular potential $V_\kappa=(\epsilon I_4 +\mu\beta+\eta(\alpha\cdot N))\delta_{\partial\Omega}$.…
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $\mathcal{C}^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the Dirac…
We consider the two-dimensional Dirac operator with Lorentz-scalar $\delta$-shell interactions on each edge of a star-graph. An orthogonal decomposition is performed which shows such an operator is unitarily equivalent to an orthogonal sum…
Let $\Omega_+\subset\mathbb{R}^{3}$ be a fixed bounded domain with boundary $\Sigma = \partial\Omega_{+}$. We consider $\mathcal{U}^\varepsilon$ a tubular neighborhood of the surface $\Sigma$ with a thickness parameter $\varepsilon>0$, and…
We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar $\delta$-interactions of constant strengths supported on a smooth closed curve. For any combination of the coupling constants a…
We study two-dimensional Dirac operators with singular interactions of electrostatic and Lorentzscalar type, supported either on a straight line or a circle. For certain critical values of the interaction strengths, the essential spectrum…
Given a bounded smooth domain $\Omega\subset\mathbb{R}^3$, we explore the relation between couplings of the free Dirac operator $-i\alpha\cdot\nabla+m\beta$ with pure electrostatic shell potentials $\lambda\delta_{\partial\Omega}$…