Related papers: Sharp bound for embedded eigenvalues of Dirac oper…

We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields:…

Let q and v be symmetric sesquilinear forms such that v is a form perturbation of q. Then we can associate a unique self-adjoint operator B to q+ v. Assuming that B has a gap (a, b) in the essential spectrum, we prove a minimax principle…

We study spectral properties of the Dirac operator $L_0$ arising as the upper-right off-diagonal block in the linearization around standing wave solutions of the one-dimensional Soler model with power nonlinearity $f(s)=s|s|^{p-1}$, $p>0$.…

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero temperature and at baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the…

We consider Schr\"odinger operators with potentials satisfying a generalized bounded variation condition at infinity and an $L^p$ decay condition. This class of potentials includes slowly decaying Wigner--von Neumann type potentials…

Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields…

In this paper, we consider the eigenvalue problem of Dirac operator on a compact Riemannian manifold isometrically immersed into Euclidean space and derive some extrinsic estimates for the sum of arbitrary consecutive $n$ eigenvalues of the…

We consider the following model of degenerate and singular oscillatory integral operators: \begin{equation*} Tf(x)=\int_{\mathbb{R}} e^{i\lambda S(x,y)}K(x,y)\psi(x,y)f(y)dy, \end{equation*} where the phase functions are homogeneous…

This paper is the first of a series where we study the spectral properties of Dirac operators with the Coulomb potential generated by any finite signed charge distribution $\mu$. We show here that the operator has a unique distinguished…

In this paper, we consider the perturbed Stark operator \begin{equation*} Hu=H_0u+qu=-u^{\prime\prime}-xu+qu, \end{equation*} where $q$ is the power-decaying perturbation. The criteria for $q$ such that $H=H_0+q$ has at most one eigenvalue…

In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are…

The purpose of this paper is to study the eigenvalues $\{\lambda_{\mu,i} \}_i$ for the Dirichlet Hardy-Leray operator, i.e. $$ -\Delta u+\mu|x|^{-2}u=\lambda u\ \ {\rm in}\ \, \Omega,\quad\quad u=0\ \ {\rm on}\ \ \partial\Omega,$$ where…

Let $L$ be the Hill operator or the one dimensional Dirac operator on the interval $[0,\pi].$ If $L$ is considered with Dirichlet, periodic or antiperiodic boundary conditions, then the corresponding spectra are discrete and for large…

We prove the discrete restriction conjecture holds with no loss when $p>\frac{2d}{d-4}$ and $d\geq 5$. That is, we show optimal $L^p$ bounds for eigenfunctions of the Laplacian on the square torus for large values of $p$. This improves the…

We obtain the uniform asymptotic formulas for the eigenvalues and eigenfunctions of the Sturm-Liouville operators L_{t}(q) with a potential q\inL_{1}[0,1] and with t-periodic boundary conditions, t\in(-{\pi},{\pi}]. Using these formulas, we…

We strengthen and generalise a result of Kirsch and Simon on the behaviour of the function $N_L(E)$, the number of bound states of the operator $L = \Delta+V$ in $\R^d$ below $-E$. Here $V$ is a bounded potential behaving asymptotically…

We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark…

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…

We prove a new upper bound for the smallest eigenvalues of the Dirac operator on a compact hypersurface of the hyperbolic space.

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…