Related papers: Domains for Dirac-Coulomb min-max levels

The self-adjointness of $H+V$ is studied, where $H=-i\alpha\cdot\nabla +m\beta$ is the free Dirac operator in $\R^3$ and $V$ is a measure-valued potential. The potentials $V$ under consideration are given by singular measures with respect…

We prove lower Dirac eigenvalue bounds for closed surfaces with a spin structure whose Arf invariant equals 1. Besides the area only one geometric quantity enters in these estimates, the spin-cut-diameter which depends on the choice of spin…

We compute the whole spectrum of the Dirichlet-to-Neumann operator acting on differential p-forms on the unit Euclidean ball. Then, we prove a new upper bound for its first eigenvalue on a domain $\Omega$ in Euclidean space in terms of the…

The Dirac equation may be thought as originating from a theory of five-dimensional (5D) space-time. We define a special 5D Clifford algebra and introduce a spin-1/2 constraint equation to describe null propagation in a 5D space-time…

We present exact analytical solutions of the Dirac equation in $(1+1)$-dimensions for the generalized Kratzer potential by taking the pseudoscalar interaction term as an attractive Coulomb potential. We study the problem for a particular…

We analyze the eigenvalue problem for the semiclassical Dirac (or Zakharov-Shabat) operator on the real line with general analytic potential. We provide Bohr-Sommerfeld quantization conditions near energy levels where the potential exhibits…

We present an explicit two-parameter family of finite-band Jacobi elliptic potentials for a non-self-adjoint Dirac operator which connects two previously known limiting cases in which the elliptic parameter is zero or one. A full…

We are concerned with the dependence of the lowest positive eigenvalue of the Dirac operator on the geometry of rectangles, subject to infinite-mass boundary conditions. We conjecture that the square is a global minimiser both under the…

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…

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 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…

We consider the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov--Bohm solenoid field and a collinear uniform magnetic field). Using von Neumann's theory of the self-adjoint extensions of symmetric operators,…

We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2].

The aim of this paper is to review and compare the spectral properties of (the closed extension of) --$\Delta$ + U (V $\ge$ 0) and --$\Delta$ + iV in L 2 (R^d) for C $\infty$ real potentials U or V with polynomial behavior. The case with…

We consider the eigenvalues of an elliptic operator for systems with bounded, measurable, and symmetric coefficients. We assume we have two non-empty, open, disjoint, and bounded sets and add a set of small measure to form the perturbed…

Analyzing the point spectrum, i.e. bound state energy eigenvalue, of the Dirac delta function in two and three dimensions is notoriously difficult without recourse to regularization or renormalization, typically both. The reason for this in…

Using three different notions of generalized principal eigenvalue of linear second order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the…

We study the distribution of the eigenvalues inside of the essential spectrum for discrete one-dimensional Schr\"odinger operators with potentials of Coulomb type decay.

We consider the three-dimensional Dirac equation in spherical coordinates with coupling to static electromagnetic potential. The space components of the potential have angular (non-central) dependence such that the Dirac equation is…

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…