Related papers: Periodic Dirac operator on the half-line
In this paper, we propose a strategy to determine the Dirichlet-to-Neumann (DtN) operator for infinite, lossy and locally perturbed hexagonal periodic media. We obtain a factorization of this operator involving two non local operators. The…
The Dirac monopole string is specified for de Sitter cosmological model. Dirac equation for spin 1/2 particle in presence of this monopole has been examined on the background of de Sitter space-time in static coordinates. Instead of spinor…
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb operator in a suitable complete square integrable basis. Orthogonal polynomials techniques along with Darboux method are used to obtain the bound states energy…
We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…
In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric $\delta (r-r_{0})$-potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of $r_{0}$ can be…
We formulate the Dirac equation for a massive neutral spin-half particle on a rotating black hole spacetime, and we consider its (quasi)bound states: gravitationally-trapped modes which are regular across the future event horizon. These…
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…
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…
We discuss a novel strategy for computing the eigenvalues and eigenfunctions of the relativistic Dirac operator with a radially symmetric potential. The virtues of this strategy lie on the fact that it avoids completely the phenomenon of…
This paper presents the spectral analysis of 1-dimensional Schroedinger operator on the half-line whose potential is a linear combination of the Coulomb term 1/r and the centrifugal term 1/r^2. The coupling constants are allowed to be…
The Dirac equation with a scalar and an electromagnetic potentials is considered. In the time-harmonic case and when all the involved functions depend only on two spatial variables it reduces to a pair of decoupled bicomplex Vekua-type…
We study the spectrum and dynamics of a one-dimensional discrete Dirac operator in a random potential obtained by damping an i.i.d. environment with an envelope of type $n^{-\alpha}$ for $\alpha>0$. We recover all the spectral regimes…
We study Schr\"odinger operators on the real line whose potentials are generated by an underlying ergodic subshift over a finite alphabet and a rule that replaces symbols by compactly supported potential pieces. We first develop the…
The half-line Dirac operators with $L^2$-potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the…
This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a…
We prove existence of solutions to boundary value problems and obstacle problems for degenerate-elliptic, linear, second-order partial differential operators with partial Dirichlet boundary conditions using a new version of the Perron…
A model in which a Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor…
The Dirac monopole string is specified for anti de Sitter cosmological model. Dirac equation for spin 1/2 particle in presence of this monopole has been examined on the background of anti de Sitter space-time in static coordinates. Instead…
We consider the magnetic Schrodinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann boundary condition…
This paper is related to an inverse problem for a class of Dirac operators with discontinuous coefficient and eigenvalue parameter contained in boundary conditions. The asymptotic formula of eigenvalues of this problem is examined. The…