Related papers: On gap properties for the linearized 1D Dirac--Sol…

In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…

We show that the lamplighter group L has a system of generators for which the spectrum of the discrete Laplacian on the Cayley graph is a union of an interval and a countable set of isolated points accumulating to a point outside this…

In [DO99,KY99], the strong unique continuation property from the origin is established for $H_{loc}^1$-solutions to the massless Dirac differential inequality $|{D}_n u | \leq \frac{C}{|x|}|u|$, in dimension $n\geq 2$ and with $C<\frac12$.…

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 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 the properties of eigenvalues and corresponding eigenfunctions generated by a defect in the gaps of the spectrum of a high-contrast random operator. We consider a family of elliptic operators $\mathcal{A}^\varepsilon$ in divergence…

We describe a new family of examples of hypersurfaces in the sphere satisfying the limiting-case in C. B\"ar's extrinsic upper bound for the smallest eigenvalue of the Dirac operator.

We consider the Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimised by the isosceles right triangle both under the area or perimeter constraints. We…

In this note the three dimensional Dirac operator $A_m$ with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that $A_m$ is self-adjoint in…

We study the (massless) Dirac operator on a 3-sphere equipped with Riemannian metric. For the standard metric the spectrum is known. In particular, the eigenvalues closest to zero are the two double eigenvalues +3/2 and -3/2. Our aim is to…

We investigate $L^1\to L^\infty$ dispersive estimates for the one dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies the natural $t^{-\frac12}$ decay rate, which may be improved to…

We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among…

We study boundary value problems for linear elliptic differential operators of order one. The underlying manifold may be noncompact, but the boundary is assumed to be compact. We require a symmetry property of the principal symbol of the…

In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…

The discovery of intriguing properties related to the Dirac states in graphene has spurred huge interest in exploring its two-dimensional group-IV counterparts, such as silicene, germanene, and stanene. However, these materials have to be…

We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed…

We numerically find out the spectrum of the $3$ spin $1$ Dirac operators found in~\cite{ApbPP}. We give an analytic and numerical proof that they are unitarily inequivalent. Since these operators come paired with an anticommuting chirality…

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An…

We prove sharp lower bounds on the spectral gap of 1-dimensional Schr\"odinger operators with Robin boundary conditions for each value of the Robin parameter. In particular, our lower bounds apply to single-well potentials with a centered…

We consider an elliptic self-adjoint first order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of our operator is…