For every closed Riemannian spin manifold its Dirac operator is a selfadjoint linear elliptic operator acting on sections of the spinor bundle. Hitchin [3] proved that the dimension of its kernel, the space of harmonic spinors, only depends on the conformal class of the Riemannian metric, and that it varies with the conformal class. However, the variation is not understood. Investigating this v...

Lower bounds on the magnitude of the spectrum of the Hermitian WilsonDirac operator H(m) have previously been derived for 0 < m < 2 when the lattice gauge field satisfies a certain smoothness condition. In this paper lower bounds are derived for 2p−2 < m < 2p for general p = 1, 2, . . . , d where d is the spacetime dimension. The bounds can alternatively be viewed as localisation bounds on the ...

In this paper, we apply Dirac structures and the associated theory of implicit Lagrangian systems to electric networks. We show how a Dirac structure on the flux linkage phase space can be induced from a KCL (Kirchhoff Current Law) constraint distribution on a configuration charge space in analogy with mechanics. In this context, a notion of implicit port–controlled Lagrangian systems is develo...

Bulk insulators with strong spin orbit coupling exhibit metallic surface states possessing topological order protected by the time reversal symmetry. However, experiments show vulnerability of topological states to aging and impurities. Different studies show contrasting behavior of the Dirac states along with plethora of anomalies, which has become an outstanding problem in material science. H...

This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator which resembles a global functional derivation operator. The interaction between the Dirac operator and the algebra reproduces the Poisson structure of Gener...

We develop (within a possibly new) framework spectral analysis and operator theory on (almost) general graphs and use it to study spectral properies of the graph-Laplacian and so-called graph-Dirac-operators. That is, we introduce a Hilbert space structure, being in our framework the direct sum of a node-Hilbert-space and a bond-Hilbert-space, a Dirac operator intertwining these components, and...

Based on the first principles calculation, we investigate the electronic band structures of graphene-MoS2 and Ti-MoS2 heterojunctions under gate-voltages. By simultaneous control of external electric fields and carrier charging concentrations, we show that the graphene's Dirac point position inside the MoS2 bandgap is easily modulated with respect to the co-varying Fermi level, while keeping th...

Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centred around the concept of monogenic functions, which constitute the kernel of a first order vector valued, rotation invariant, differential operator ∂ called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has ...

The DIRAC system was developed in order to provide a complete solution for using the distributed computing resources of the LHCb experiment at CERN for data production and analysis. It allows a concurrent use of over 10K CPUs and 10M file replicas distributed over many tens of sites. The sites can be part of a Computing Grid such as WLCG or standalone computing clusters all integrated in a sing...

The subject of topological materials has attracted immense attention in condensed-matter physics because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones e...