Related papers: Eigenvalue estimates for the Dirac operator and ha…

Estimates for eigenvalues of Schr\"{o}dinger operators on the half-line with complex-valued potentials are established. Schr\"{o}dinger operators with potentials belonging to weak Lebesque's classes are also considered. The results cover…

Withdrawn by author due to copyright transfer. See: http://www3.interscience.wiley.com/cgi-bin/abstract/116836954/ABSTRACT

This paper has been withdrawn by the author. An assumption made in the analysis is not valid under the experimental conditions.

A perturbation decaying to 0 at infinity and not too irregular at 0 introduces at most a discrete set of eigenvalues into the spectral gaps of a one-dimensional Dirac operator on the half-line. We show that the number of these eigenvalues…

The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968

We exploit the connection between quantum dot Dirac operators and $\overline\partial$-Robin Laplacians. First, we find a graphical relation between their smallest positive eigenvalues, which allows us to deduce a recipe for translating…

The paper has been withdrawn

This paper was withdrawn by the authors due an error in the elimination of the front in the linearized interior equations (28)-(29).

This paper has been withdrawn by the authors due to an incorrect analysis.

This submission has been withdrawn by the authors because it is a duplicate of arXiv:hep-ph/0611336. It was due to a technical submission error by the authors.

This paper has been withdrawn by the authors; the main conclusion is incorrect, as some of the crucial calculations were not properly converged.

We define (higher rank) spinorially twisted spin structures and deduce various curvature identites as well as estimates for the eigenvalues of the corresponding twisted Dirac operators.

Following Escobar [Esc97] and Jammes [Jam15], we introduce two types of isoperimetric constants and give lower bound estimates for the first nontrivial eigenvalues of Dirichlet-to-Neumann operators on finite graphs with boundary…

We consider the 3-dimensional Stark operator perturbed by a complex-valued potential. We obtain an estimate for the number of eigenvalues of this operator as well as for the sum of imaginary parts of eigenvalues situated in the upper…

We tried to determine the range of validity of a recently proposed modification of the Hellmann potential that leads to analytical eigenvalues and eigenfunctions. We discuss the difficulties that we found in the analysis of the main…

We provide eigenvalue asymptotics for a Dirac-type operator on $\mathbb Z^n$, $n\geq 2$, perturbed by multiplication operators that decay as $|\mu|^{-\gamma}$ with $\gamma<n$. We show that the eigenvalues accumulate near the value of the…

We consider a Dirac operator in three space dimensions, with an electrostatic (i.e. real-valued) potential $V(x)$, having a strong Coulomb-type singularity at the origin. This operator is not always essentially self-adjoint but admits a…

The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…

The paper has been withdrawn by the author.

This paper has been withdrawn by the authors because the analysis has been extended in Ref.(arXiv:0804.1252) to the sbottom-antisbottom case.