Related papers: Spectral Asymptotic for the Infinite Mass Dirac Op…
We consider a two-dimensional massless Dirac operator coupled to a magnetic field $B$ and an electric potential $V$ growing at infinity. We find a characterization of the spectrum of the resulting operator $H$ in terms of the relation…
We study a self-adjoint realization of a massless Dirac operator on a bounded connected domain $\Omega\subset \mathbb{R}^2$ which is frequently used to model graphene quantum dots. In particular, we show that this operator is the limit, as…
In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…
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 $V_\kappa=(\epsilon I_4 +\mu\beta+\eta(\alpha\cdot N))\delta_{\partial\Omega}$.…
In this work we study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular to the plane. We focus on the infinite-mass boundary condition (also called MIT bag condition). In the case of bounded domains, we…
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a…
Given an open set $\Omega\subset\mathbb{R}^3$. We deal with the spectral study of Dirac operators of the form $H_{a,\tau}=H+A_{a,\tau}\delta_{\partial\Omega}$, where $H$ is the free Dirac operator in $\mathbb{R}^3$, $A_{a,\tau}$ is a…
We consider a 3-dimensional Dirac operator H_0 with non-constant magnetic field of constant direction, perturbed by a sign-definite matrix-valued potential V decaying fast enough at infinity. Then we determine asymptotics, as the energy…
We investigate the spectrum of the Dirac operator with infinite mass boundary conditions posed in a tubular neighborhood of a smooth compact hypersurface in $\mathbb{R}^n$ without boundary. We prove that when the tubular neighborhood…
The one-dimensional Dirac operator \begin{equation*} L = i \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \frac{d}{dx} +\begin{pmatrix} 0 & P(x) \\ Q(x) & 0 \end{pmatrix}, \quad P,Q \in L^2 ([0,\pi]), \end{equation*} considered on $[0,\pi]$…
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary…
Spectral properties and the confinement phenomenon for the coupling $H+V$ are studied, where $H=-i\alpha\cdot\nabla +m\beta$ is the free Dirac operator in $\mathcal{R}^3$ and $V$ is a measure-valued potential. The potentials $V$ under…
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to…
In this paper we present a complete spectral analysis of Dirac operators with non-Hermitian matrix potentials of the form $i\operatorname{sgn}(x)+V(x)$ where $V\in L^1$. For $V=0$ we compute explicitly the matrix Green function. This allows…
In this paper, we study the spectrality of the non-self-adjoint Dirac operator L(Q) with a complex-valued periodic matrix potential Q. We establish a condition on the off-diagonal elements of the matrix Q under which L(Q) is an…
The spectral and scattering theory for 1-dimensional Dirac operators with mass $m$ and with zero-range interactions are fully investigated. Explicit expressions for the wave operators and for the scattering operator are provided. These new…
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…
In this paper we investigate the spectrum of the Dirac operator posed in a tubular neighborhood of a planar loop with infinite mass boundary conditions. We show that when thewidth of the tubular neighborhood goes to zero the asymptotic…
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 absence of point spectrum. In the massless case, our approach…