Related papers: Estimates on complex eigenvalues for Dirac operato…
We give a new upper bound for the smallest eigenvalues of the Dirac operator on a Riemannian flow carrying transversal Killing spinors. We derive an estimate on Sasakian and on 3-dimensional manifolds and partially classify those satisfying…
Eigenvalue problems for semidefinite operators with infinite dimensional kernels appear for instance in electromagnetics. Variational discretizations with edge elements have long been analyzed in terms of a discrete compactness property. As…
Using a correspondence between the spectrum of the damped wave equation and non-self-adjoint Schroedinger operators, we derive various bounds on complex eigenvalues of the former. In particular, we establish a sharp result that the…
We discuss the behaviour of the spectral density of the massless Dirac operator at the small eigenvalues and quark masses compatible with the restrictions imposed by the low energy theorems in QCD. Sum rule for its derivative over the quark…
We establish an upper estimate for the small eigenvalues of the twisted Dirac operator on Kahler submanifolds in Kahler manifolds carrying Kahlerian Killing spinors. We then compute the spectrum of the twisted Dirac operator of the…
It has recently been conjectured that the eigenvalues $\lambda$ of the Dirac operator on a closed Riemannian spin manifold $M$ of dimension $n\ge 3$ can be estimated from below by the total scalar curvature: $$ \lambda^2 \ge…
In this paper we study the self-adjointness and spectral properties of two-dimensional Dirac operators with electrostatic, Lorentz scalar, and anomalous magnetic $\delta$-shell interactions with constant weights that are supported on a…
The eigenvalue spectrum $\rho(\lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract…
We consider an elliptic self-adjoint first order differential operator L acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of the operator L…
We give a survey of results relating the restricted holonomy of a Riemannian spin manifold with lower bounds on the spectrum of its Dirac operator, giving a new proof of a result originally due to Kirchberg.
We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions, we demonstrate the equivalence between the essential…
We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The…
We study a self-adjoint realization of a massless Dirac operator on a bounded connected domain $\Omega\subset \mathbb{R}^2$ which is frequently used to model graphene quantum dots. In particular, we show that this operator is the limit, as…
We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are…
We establish Lieb-Thirring type inequalities for non self-adjoint relatively compact perturbations of certain operators of mathematical physics. We apply our results to quantum Hamiltonians of Schr{\"o}dinger and Pauli with constant…
The self-conjugate Dirac Hamiltonian is obtained in the Kerr-Newman field. A transition is implemented to a Schr\"odinger-type relativistic equation. For the case where the angular and radial variables are not separated, the method of…
We investigate $L^1\to L^\infty$ dispersive estimates for the three dimensional Dirac equation with a potential. We also classify the structure of obstructions at the thresholds of the essential spectrum as being composed of a two…
We consider Dirac, Pauli and Schr\"odinger quantum magnetic Hamiltonians of full rank in ${\rm L}^2 \big(\mathbb{R}^{2d} \big)$, $d \ge 1$, perturbed by non-self-adjoint (matrix-valued) potentials. On the one hand, we show the existence of…
We discuss resonances for 1D massless Dirac operators with compactly supported potentials on the line. We estimate the sum of the negative power of all resonances in terms of the norm of the potential and the diameter of its support.
Sharp resolvent bounds for non-selfadjoint semiclassical elliptic quadratic differential operators are established, in the interior of the range of the associated quadratic symbol.