We discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition , charge conjugation, hypercubic rotations and reflections) on the lattice. We give an extensive set of examples and offer help to add further structures.

Let M be a closed connected spin manifold of dimension 2 or 3 with a fixed orientation and a fixed spin structure. We prove that for a generic Riemannian metric onM the non-harmonic eigenspinors of the Dirac operator are nowhere zero. The proof is based on a transversality theorem and the unique continuation property of the Dirac operator.

Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic ...

Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic...

In this paper, model reference neural network structure is used as a controller for vibration suppression of the Euler–Bernoulli beam under the excitation of moving mass travelling along a vibrating path. The non-dimensional equation of motion the beam acted upon by a moving mass is achieved.  A Dirac-delta function is used to describe the position of the moving mass along the beam and its iner...

The dynamical property of electrons with the tilted Dirac cone was examined using the tilted Weyl equation. The polarization function exhibits cusps and nonmonotonic structures by varying both the frequency and the momentum. A pair of tilted Dirac cones exhibits a new plasmon for the intermediate magnitude of momentum owing to the combined effects of two tilted cones. Dirac electrons with the z...

We consider the local chirality of near-zero eigenvectors from Wilson-Dirac and clover improved Wilson-Dirac lattice operators as proposed recently by Horváth et al. We studied finer lattices and repaired for the loss of orthogonality due to the non-normality of the Wilson-Dirac matrix. As a result we do see a clear double peak structure on lattices with resolutions higher than 0.1 fm. We found...

A moiré pattern is formed when two copies of a periodic pattern are overlaid with a relative twist. We address the electronic structure of a twisted two-layer graphene system, showing that in its continuum Dirac model the moiré pattern periodicity leads to moiré Bloch bands. The two layers become more strongly coupled and the Dirac velocity crosses zero several times as the twist angle is reduc...

Using a structural search method in combination with first-principles calculations, we found lots of low energy 2D carbon allotropes and examined all possible Dirac points around their Fermi levels. Three amazing 2D Dirac carbon allotropes have been discovered, named as S-graphene, D-graphene and E-graphene. By analyzing the topology correlations among S-, T, net W graphene and graphene, we fou...

A generalization of the pseudoclassical action of a spinning particle in the presence of an anomalous magnetic momentum is given. The action is written in reparametrization and supergauge invariant form. The Dirac quantization, based on the Hamiltonian analyses of the model, leads to the Dirac-Pauli equation for a particle with an anomalous magnetic momentum in an external electromagnetic field...