Related papers: Spectrum of the wave equation with Dirac damping o…
We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that the non-self-adjoint generator of the evolution problem…
A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an $\alpha$-multiple of the Dirac $\delta$-type damping, is derived. Depending on the choice of the…
We study the spectrum of a self-adjoint Dirac-Krein operator with potential on a compact star graph $\mathcal G$ with a finite number $n$ of edges. This operator is defined by a Dirac-Krein differential expression with summable matrix…
We evaluate the spectral determinant for the damped wave equation on an interval of length $T$ with Dirichlet boundary conditions, proving that it does not depend on the damping. This is achieved by analysing the square of the damped wave…
Spectral problem for the Dirac operator with regular but not strongly regular boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper is to find conditions under which the…
One dimensional Dirac operators $$ L_{bc}(v) y = i 1 & 0 0 & -1 \frac{dy}{dx} + v(x) y, \quad y = y_1 y_2, \quad x\in[0,\pi]$$, considered with $L^2$-potentials $ v(x) = 0 & P(x) Q(x) & 0$ and subject to regular boundary conditions ($bc$),…
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 determine conditions for the quantisation of graphs using the Dirac operator for both two and four component spinors. According to the Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry the energy level…
In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…
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…
The discrete spectrum of the Dirac operator for a point electron in the maximal analytically extended Kerr--Newman spacetime is determined in the zero-$G$ limit (z$G$KN), under some restrictions on the electrical coupling constant and on…
In this paper we present a complete spectral analysis of Dirac operators with non-Hermitian matrix potentials of the form $i\operatorname{sgn}(x)+V(x)$ where $V\in L^1$. For $V=0$ we compute explicitly the matrix Green function. This allows…
The paper is concerned with the completeness property of root functions of general boundary value problems for $n \times n$ first order systems of ordinary differential equations on a finite interval. In comparison with the recent paper…
It is a well-known fact that on a bounded spectral interval the Dirac spectrum can be described locally by a non-decreasing sequence of continuous functions of the Riemannian metric. In the present article we extend this result to a global…
Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive a general inequality depending on a real parameter and joining the spectrum of the Dirac operator with terms depending on the Ricci tensor and its first…
We consider the magnetic Schrodinger operator in a two-dimensional strip. On the boundary of the strip the Dirichlet boundary condition is imposed except for a fixed segment (window), where it switches to magnetic Neumann boundary condition…
We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the…
We consider a complete Riemannian manifold, which consists of a compact interior and one or more $\varphi$-cusps: infinitely long ends of a type that includes cylindrical ends and hyperbolic cusps. Here $\varphi$ is a function of the radial…
We analyze the limit of the spectrum of a geometric Dirac-type operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by 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…