Related papers: Spectral analysis of the Dirac operator on a 3-sph…

We show that the spectrum of the curl operator on a generic smoothly bounded domain in three-dimensional Euclidean space consists of simple eigenvalues. The main new ingredient in our proof is a formula for the variation of curl eigenvalues…

This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions…

Let $(M_i, g_i)_{i \in \mathbb{N}}$ be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower dimensional Riemannian manifold $(B,h)$ in the Gromov-Hausdorff topology. Lott showed that the…

Let $M$ be a closed connected spin manifold such that its spinor Dirac operator has non-vanishing (Rosenberg) index. We prove that for any Riemannian metric on $V = M \times [-1,1]$ with scalar curvature bounded below by $\sigma > 0$, the…

The paper is devoted to investigation of the spectrum of a perturbed Laplace-Beltrami operator on manifolds with closed geodesics of the same length and where metric is a perturbation of the metric of the unit sphere. As the result, we give…

We derive new perturbation bounds for eigenvalues of Hermitian matrices with block structures. The structures we consider range from a standard 2-by-2 block form to block tridiagonal and tridigaonal forms. The main idea is the observation…

The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low--energy correlation functions of…

We re-visit the eigenvalue estimate of the Dirac operator on spin manifolds with boundary in terms of the first eigenvalues of conformal Laplace operator as well as the conformal mean curvature operator. These problems were studied earlier…

We study the spectrum of the staggered Dirac operator in SU(2) gauge fields close to the free limit, for both the fundamental and the adjoint representation. Numerically we find a characteristic cluster structure with spacings of adjacent…

We investigate the spectrum of three-dimensional Schr\"{o}dinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues below the…

As an outgrowth of our investigation of non-regular spaces within the context of quantum gravity and non-commutative geometry, we develop a graph Hilbert space framework on arbitrary (infinite) graphs and use it to study spectral properties…

The purpose of this paper is to explore the asymptotics of the eigenvalue spectrum of the Laplacian on 2 dimensional spaces of constant curvature, giving strong experimental evidence for a conjecture of the second author…

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…

The one-dimensional Dirac operator with periodic potential $V=\begin{pmatrix} 0 & \mathcal{P}(x) \\ \mathcal{Q}(x) & 0 \end{pmatrix}$, where $\mathcal{P},\mathcal{Q}\in L^2([0,\pi])$ subject to periodic, antiperiodic or a general strictly…

Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac…

For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…

We study the spectrum of the Dirichlet Laplacian operator in a two-dimensional twisted strip embedded in $\mathbb R^d$ with $d \geq 2$. It is shown that a local twisting perturbation can create discrete eigenvalues for the operator. In…

We investigate the spectral properties of a random matrix model, which in the large $N$ limit, embodies the essentials of the QCD partition function at low energy. The exact spectral density and its pair correlation function are derived for…

We solve for the spectrum and eigenfunctions of Dirac operator on the sphere. The eigenvalues are nonzero whole numbers. The eigenfunctions are two-component spinors which may be classified by representations of the SU(2) group with…

When a Riemannian manifold $(M,g)$ is rotationally symmetric, the critical order of the lower bound of radial curvatures for the absence of eigenvalues of the Laplacian is equal to $ -\frac{1}{r}$, where $r$ stands for the distance to the…