Related papers: Diffraction of weighted lattice subsets

In the continuum, a topological obstruction to the vanishing of the non-abelian anomaly in 2n dimensions is given by the index of a certain Dirac operator in 2n+2 dimensions, or equivalently, the index of a 2-parameter family of Dirac…

The pinwheel tiling is the paradigm for a substitution tiling with circular symmetry, in the sense that the corresponding autocorrelation is circularly symmetric. As a consequence, its diffraction measure is also circularly symmetric, so…

The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated, and characterized up to a measure zero set, by means of the Bombieri-Taylor conjecture, for Bragg peaks, and of another conjecture that we call…

We analyze newly expanded and refined data from lattice studies of an SU(3) gauge theory with eight Dirac fermions in the fundamental representation. We focus on the light composite states emerging from these studies, consisting of a set of…

Particle fractionalization is believed to orchestrate the physics of many strongly correlated systems, yet its direct experimental detection remains a challenge. We propose a simple measurement for an ultracold matter system, in which…

We show that multiple layered Dirac cones can emerge in the band structure of properly addressed multicomponent cold fermionic gases in optical lattices. The layered Dirac cones contain multiple copies of massless spin-1/2 Dirac fermions at…

We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix…

The transmission poles of $N$ number of identical Dirac delta potentials placed periodically in one-dimension are examined in the complex-energy plane. The numerical results show that the imaginary part of the poles scales with 1/N. An…

We explore the collective density oscillations of a collection of charged massive Dirac particles, in one, two and three dimensions and their one dimensional superlattice. We calculate the long wavelength limit of the dynamical polarization…

We study the uniform ergodicity property for non-invertible topological and measure-preserving dynamical systems. It is shown that for topological dynamical systems uniform ergodicity is equivalent to eventually periodicity and that for…

Periodic photonic structures enable precise control over the light-matter interaction through band structure engineering. Certain lattice geometries exhibit dispersionless flat bands, characterized by vanishing group velocity and diverging…

We study topological properties of classical spherical center vortices with the low-lying eigenmodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations. In…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

The Talbot effect, epitomized by periodic revivals of a freely evolving periodic field structure, has been observed with waves of diverse physical nature in space and separately in time, whereby diffraction underlies the former and…

We study the dynamics of ultracold atoms in tailored bichromatic optical lattices. By tuning the lattice parameters, one can readily engineer the band structure and realize a Dirac point, i.e. a true crossing of two Bloch bands. The…

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the…

Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of…

Electron properties of graphene are described in terms of Dirac fermions. Here we thoroughly outline the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential. While the…

Dirac fermions on a two-dimensional lattice with disorder are considered. The Dirac mass, which controls the gap between the two bands of the fermions, is subject to random fluctuations. Another type of disorder is discussed presented by a…

In a recent article [10], the authors proved that the non-relativistic Schr\"odinger operator with a generic honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta,…