Related papers: Non-self-adjoint Dirac operators on graphs
We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…
We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance…
On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity…
We analyze eigenvalues emerging from thresholds of the essential spectrum of one-dimensional Dirac operators perturbed by complex and non-symmetric potentials. In the general non-self-adjoint setting we establish the existence and…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
We study the spectrum of a periodic non-self-adjoint Dirac operator, and its dependence on a semiclassical parameter is also considered. Several bounds on the spectrum are obtained which provide sharp spectral enclosure estimates.…
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 consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
We introduce the notion of a pre-spectral triple, which is a generalisation of a spectral triple $(\mathcal{A}, H, D)$ where $D$ is no longer required to be self-adjoint, but closed and symmetric. Despite having weaker assumptions,…
The one-dimensional Dirac operator with a singular interaction term which is formally given by $A\otimes|\delta_0\rangle\langle\delta_0|$, where $A$ is an arbitrary $2\times 2$ matrix and $\delta_0$ stands for the Dirac distribution, is…
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 consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schr\"odinger operator on a star-graph with a finite number of…
We study extensions of direct sums of symmetric operators $S=\oplus_{n\in\mathbb{N}} S_n$. In general there is no natural boundary triplet for $S^*$ even if there is one for every $S_n^*$, $n\in\mathbb{N}$. We consider a subclass of…
In this paper the spectral and scattering properties of a family of self-adjoint Dirac operators in $L^2(\Omega; \mathbb{C}^4)$, where $\Omega \subset \mathbb{R}^3$ is either a bounded or an unbounded domain with a compact $C^2$-smooth…
In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…
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…
In this note we present some properties of the Dirac operator on noncompact metric graphs with Kirchoff-type vertex conditions. In particular, we discuss the specific features of the spectrum of the operator and, finally, we give some…
The necessary and sufficient conditions are given for a sequence of complex numbers to be the periodic (or antiperiodic) spectrum of non-self-adjoint Dirac operator.
We consider boundary conditions at the vertex of a star graph which make Schroedinger operators on the graph self-adjoint, in particular, the two-parameter family of such conditions invariant with respect to permutations of graph edges. It…
This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…