Related papers: Existence of Dirac resonances in the semi-classica…
We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via…
We consider the one-dimensional Dirac equation with the most general relativistic contact interaction supported on two points symmetrically located with respect to the origin. In order to determine the shape of the interaction, we use a…
Using the chirally invariant overlap Dirac operator we remove its lowest-lying quasizero modes from the valence quark propagators and study evolution of isovector mesons with J=1. At the truncation level about 50 MeV SU(2)_L \times SU(2)_R…
The paper deals with the Dirac operator generated on the finite interval $[0,\pi]$ by the differential expression $-B\mathbf{y}'+Q(x)\mathbf{y}$, where $$ B=\begin{pmatrix}0&1\\-1&0\end{pmatrix},\qquad…
Dirac cones are conical singularities that occur near the degenerate points in band structures. Such singularities result in enormous unusual phenomena of the corresponding physical systems. This work investigates double Dirac cones that…
We analyze in detail the analytical solutions of the Dirac equation with scalar S and vector V Coulomb radial potentials near the limit of spin and pseudospin symmetries, i.e., when those potentials have the same magnitude and either the…
We shall investigate the asymptotic behavior of the extended resolvent R(s) of the Dirac operator as |s| increases to infinity, where s is a real parameter. It will be shown that the norm of R(s), as a bounded operator between two weighted…
We derive upper eigenvalue bounds for the Dirac operator of a closed hypersurface in a manifold with Killing spinors such as Euclidean space, spheres or hyperbolic space. The bounds involve the Willmore functional. Relations with the…
We introduce a general framework for the study of the diffraction of waves by cone points at high frequencies. We prove that semiclassical regularity propagates through cone points with an almost sharp loss even when the underlying operator…
This paper is the first of a series where we study the spectral properties of Dirac operators with the Coulomb potential generated by any finite signed charge distribution $\mu$. We show here that the operator has a unique distinguished…
Depending on the behaviour of the complex-valued electromagnetic potential in the neighbourhood of infinity, pseudomodes of one-dimensional Dirac operators corresponding to large pseudoeigenvalues are constructed. This is a first systematic…
We carry out the spectral analysis of singular 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 perturbations, we…
We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class generalizing that of Killing spinors. We…
We reconstruct the rank-one, singular (point-like) perturbations of the $d$-dimensional fractional Laplacian in the physically meaningful norm-resolvent limit of fractional Schr\"{o}dinger operators with regular potentials centred around…
Dispersive time-decay estimates are proved for a one-parameter family of one-dimensional Dirac Hamiltonians with dislocations; these are operators which interpolate between two phase-shifted massive Dirac Hamiltonians at $x=+\infty$ and…
In the context of some deformed canonical commutation relations leading to isotropic nonzero minimal uncertainties in the position coordinates, a Dirac equation is exactly solved for the first time, namely that corresponding to the Dirac…
In this paper, we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary. Furthermore, we provide the proof of the Dabrowski-Sitarz-Zalecki type theorems associated with the spectral…
In this survey we gather recent results on Dirac operators coupled with $\delta$-shell interactions. We start by discussing recent advances regarding the question of self-adjointness for these operators. Afterward we switch to an…
The complex scaling method is applied to study the resonances of a Dirac particle in a Morse potential. The applicability of the method is demonstrated with the results compared with the available data. It is shown that the present…
The general Dirac equation in 1+1 dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector-scalar-pseudoscalar square potentials, the states of relativistic fermions are investigated. This…