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The spectral gap of the graph Laplacian with Dirichlet boundary conditions is computed for the graphs of several communication networks at the IP-layer, which are subgraphs of the much larger global IP-layer network. We show that the…
We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation…
We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate…
We investigate the index of the Neuberger's Dirac operator in abelian gauge theories on finite lattices by numerically analyzing the spectrum of the hermitian Wilson-Dirac operator for a continuous family of gauge fields connecting…
A rose graph is a graph consisting of cycles that all meet in one vertex. We show that except for two specific examples, these rose graphs are determined by the Laplacian spectrum, thus proving a conjecture posed by Lui and Huang [F.J. Liu…
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…
We derive the spectrum of the Dirac operator for the linear sigma-model with quarks in the large N_c approximation using renormalization group flow equations. For small eigenvalues, the Banks-Casher relation and the vanishing linear term…
Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major…
We study the non-selfadjoint Dirac system on the line having an non-integrable regular singularity in an interior point with additional matching conditions at the singular point. Special fundamental systems of solutions are constructed with…
The statistical properties of the spectrum of the staggered Dirac operator in an SU(2) lattice gauge theory are analyzed both in the bulk of the spectrum and at the spectrum edge. Two commonly used statistics, the number variance and the…
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…
The aim of the present paper is to analyse the spectrum of Laplace and Dirac type operators on metric graphs. In particular, we show for equilateral graphs how the spectrum (up to exceptional eigenvalues) can be described by a natural…
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary…
Let $Y$ be a compact, oriented 3-manifold with a contact form $a$ and a metric $ds^2$. Suppose that $F\to Y$ is a principal bundle with structure group $U(2) = SU(2)\times_{\pm1}S^1$ such that $F/S^1$ is the principal SO(3) bundle of…
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…
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…
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
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…
The aim of the present paper is to introduce the notion of first order (supersymmetric) Dirac operators on discrete and metric (``quantum'') graphs. In order to cover all self-adjoint boundary conditions for the associated metric graph…
We give the first example of a connected 4-regular graph whose Laplace operator's spectrum is a Cantor set, as well as several other computations of spectra following a common ``finite approximation'' method. These spectra are simple…