Related papers: Exceptional coupling constants for the Coulomb-Dir…
In this note the three dimensional Dirac operator $A_m$ with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that $A_m$ is self-adjoint in…
This paper is devoted to the study of the two-dimensional Dirac-Coulomb operator in presence of an Aharonov-Bohm external magnetic potential. We characterize the highest intensity of the magnetic field for which a two-dimensional magnetic…
In [DO99,KY99], the strong unique continuation property from the origin is established for $H_{loc}^1$-solutions to the massless Dirac differential inequality $|{D}_n u | \leq \frac{C}{|x|}|u|$, in dimension $n\geq 2$ and with $C<\frac12$.…
The present paper studies the Dirac Hamiltonian of a test electron with a domain of bi-spinor wave functions supported on the static region inside the Cauchy horizon of the subextremal RWN black hole spacetime, respectively inside the event…
We study the effect of the long-range Coulomb interaction in $j=3/2$ Dirac electrons in cubic crystals with the $O_h$ symmetry, which serves as an effective model for antiperovskite topological crystalline insulators. The renormalization…
The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…
The Dirac equation for a massive spin-1/2 field in a central potential V in three dimensions is studied without fixing a priori the functional form of V. The second-order equations for the radial parts of the spinor wave function are shown…
We consider a self-adjoint operator $T$ on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of $T$ and on the bounded perturbation $V$…
We study the stability of the one electron atom Schr\"odinger model with self-generated magnetic field in two dimensions. The magnetic energy is taken of the general form $K\int_{\mathbb{R}^2} |B|^p$ and we study the stability of the model…
We derive a classification of the self-adjoint extensions of the three-dimensional Dirac-Coulomb operator in the critical regime of the Coulomb coupling. Our approach is solely based upon the Kre{\u\i}n-Vi\v{s}ik-Birman extension scheme, or…
In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint…
In this paper we present exact solutions of the Dirac equation on the non-commutative plane in the presence of crossed electric and magnetic fields. In the standard commutative plane such a system is known to exhibit contraction of Landau…
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 the linear Dirac operator with a (-1)-homogeneous locally periodic potential that varies with respect to a small parameter. Using the notation of G-convergence for positive self-adjoint operators in Hilbert spaces we prove…
We explore the Hamiltonian operator H=-d^2/dx^2 + z \delta(x) where x is real, \delta(x) is the Dirac delta function, and z is an arbitrary complex coupling constant. For a purely imaginary z, H has a (real) spectral singularity at…
For $\nu\in[0, 1]$ let $D^\nu$ be the distinguished self-adjoint realisation of the three-dimensional Coulomb-Dirac operator $-\mathrm i\boldsymbol\alpha\cdot\nabla -\nu|\cdot|^{-1}$. For $\nu\in[0, 1)$ we prove the lower bound of the form…
A new class of lattice Dirac operators which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands…
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…
We study the spectrum of the Dirac hamiltonian in one space dimension for a single electron in the electrostatic potential of a point nucleus, in the Born-Oppenheimer approximation where the nucleus is assumed fixed at the origin. The…
We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…