相关论文: Diffraction of weighted lattice subsets

We prove that the set of visible points of any lattice of dimension at least 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the…

We investigated the properties of dichroic cholesteric liquid crystals (CLCs) being in external static magnetic field directed along helix axis. We have shown that in the case of the wavelength dependence of magneto-optic activity…

We generalize a proposal by Sorensen et al. [Phys. Rev. Lett. 94, 086803 (2005)] for creating an artificial magnetic field in a cold atom system on a square optical lattice. This leads us to an effective lattice model with tunable spatially…

The pairing properties of ultracold fermions, with an attractive interaction, loaded in a honeycomb (graphene-like) optical lattice are studied in a mean-field approach. We emphasize, in the presence of a harmonic trap, the unambiguous…

The opacity of graphene is known to be approximately given by the fine-structure constant $\alpha$ times $\pi$. We point out the fact that the opacity is roughly independent of the frequency and polarization of the light can be attributed…

Diffraction methods are at the heart of structure determination of solids. While Bragg-like scattering (pure point diffraction) is a characteristic feature of crystals and quasicrystals, it is not straightforward to interpret continuous…

Among the many families of nonperiodic tilings known so far, SCD tilings are still a bit mysterious. Here, we determine the diffraction spectra of point sets derived from SCD tilings and show that they have no absolutely continuous part,…

The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…

We study under which general conditions a pair of Dirac points in the electronic spectrum of a two-dimensional crystal may merge into a single one. The merging signals a topological transition between a semi-metallic phase and a band…

We deduce the structure of the Dirac field on the lattice from the discrete version of differential geometry and from the representation of the integral Lorentz transformations. The analysis of the induced representations of the Poincare…

We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to…

Let G be a torsion free discrete group with a finite dimensional classifying space BG. We show that G has a dual Dirac morphism if and only if a certain coarse (co)-assembly map is an isomorphism. Hence the existence of a dual Dirac…

Within a Kubo formalism, we calculate the absorptive part of the dynamic longitudinal conductivity $\sigma(\Omega)$ of a 2D semi-Dirac material. In the clean limit, we provide separate analytic formulas for intraband (Drude) and interband…

We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of…

Consequences of different discretizations of the two-dimensional Dirac operator on low energy properties (e.g., the number of nodes) and their relations to gauge properties are discussed. Breaking of the gauge invariance was suggested in a…

Cocompactness is a useful weaker counterpart of compactness in the study of imbeddings between function spaces. In this paper we show that subcritical continuous imbeddings of fractional Sobolev spaces and Besov spaces over \mathbb{R}^{N}…

An SU(2) gauge theory with two fermions transforming under the adjoint representation of the gauge group may appear conformal or almost conformal in the infrared. We use lattice simulations to study the spectrum of this theory and present…

After the discovery of graphene and its many fascinating properties, there has been a growing interest for the study of "artificial graphenes". These are totally different and novel systems which bear exciting similarities with graphene.…

Two-dimensional (2D) massless Dirac electrons appear on a surface of three-dimensional topological insulators. The conductivity of such a 2D Dirac electron system is studied for strong topological insulators in the case of the Fermi level…

Resonance coupling in non-Hermitian systems can lead to exotic features, such as bound states in the continuum (BICs) and exceptional points (EPs), which have been widely employed to control the propagation and scattering of light. Yet,…