Related papers: On gap properties for the linearized 1D Dirac--Sol…
Graphene-based superlattice (SL) formed by a periodic gap modulation is studied theoretically using a Dirac-type Hamiltonian. Analyzing the dispersion relation we have found that new Dirac points arise in the electronic spectrum under…
We develop relative oscillation theory for one-dimensional Dirac operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing…
We investigate dispersive estimates for the two dimensional Dirac equation with a potential. In particular, we show that the Dirac evolution satisfies a $t^{-1}$ decay rate as an operator from the Hardy space $H^1$ to $BMO$, the space of…
We study the spectral gap of the Erd\H{o}s--R\'enyi random graph through the connectivity threshold. In particular, we show that for any fixed $\delta > 0$ if $$p \ge \frac{(1/2 + \delta) \log n}{n},$$ then the normalized graph Laplacian of…
In this paper, we consider a discontinuous Dirac operator with eigenparameter dependent both boundary and two transmission conditions. We introduce a suitable Hilbert space formulation and get some properties of eigenvalues and…
In this paper, we consider a discontinuous Dirac operator depending polynomially on the spectral parameter and a finite number of transmission conditions. We get some properties of eigenvalues and eigenfunctions. Then, we investigate some…
We study fundamental spectral properties of random block operators that are common in the physical modelling of mesoscopic disordered systems such as dirty superconductors. Our results include ergodic properties, the location of the…
The momentum space of topological insulators and topological superconductors is equipped with a quantum metric defined from the overlap of neighboring valence band states or quasihole states. We investigate the quantum geometrical…
Recent progress in topological insulators and topological phases of matter has motivated new methods for the localization of waves in photonic structures. Especially, it is established that a Dirac point of a periodic structure can…
Let A be an n x n symmetric random matrix whose upper-triangular entries are independent and follow possibly non-identical subgaussian distributions. This paper investigates the spectral properties of A, including its eigenvalues and…
The energy spectra for the tight-binding models on the Lieb and kagom\'e lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band…
We consider the Schr\"odinger operator on zigzag graphs with a periodic potential. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite number of eigenvalues with infinite…
The system of equations for water waves, when linearized about equilibrium of a fluid body with a varying bottom boundary, is described by a spectral problem for the Dirichlet -- Neumann operator of the unperturbed free surface. This…
$1+1$-dimensional Dirac oscillator with minimal uncertainty in position and maximal in momentum is investigated. To obtain energy spectrum SUSY QM technique is applied. It is shown that the Dirac oscillator has two branches of spectrum, the…
In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint…
This work is concerned with the Dirac points for the honeycomb lattice with impenetrable obstacles arranged periodically in a homogeneous medium. We consider both the Dirichlet and Neumann eigenvalue problems and prove the existence of…
The paper is concerned with the Dirichlet spectrum $\Lambda^{a,b}_p(0,L)$ of the anisotropic $p$-Laplace operator $- \Delta^{a,b}_{p}$ on an interval $(0,L)$ where \[ \Delta^{a,b}_p u:=…
In a previous paper we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kaehler manifolds. In the present article we show that the only manifolds in the limit case, i.e. the only manifolds where the lower bound is…
We study the decay rate of the zero modes of the Dirac operator with a matrix-valued potential that is considered here without any regularity assumptions, compared to the existing literature. For the Dirac operator and for Clifford-valued…
We propose a method for finding gaps in the spectrum of a differential operator. When applied to the one-dimensional Hamiltonian of the quartic oscillator, a simple algebraic algorithm is proposed that, step by step, separates with a…