Two-dimensional parabolic Dirac system in the presence of nonmagnetic and magnetic impurities

We theoretically investigate the effect of the nonmagnetic and magnetic impurities to the 2D parabolic Dirac system. The induced charge density by the charged impurity is obtained by the linear response theory within the random phase approximation. We also calculate in-detail, the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction between two magnetic impurities placed within the 2D sheet of the Dirac materials with isotropic and anisotropic dispersion. For the anisotropic dispersion, the RKKY interaction is also anisotropic and related to the lattice parameters which can be obtained through the DFT calculation or the experiments. The features of the RKKY interaction also can be treated as a signature of the topological phase transition as well as the change of Berry curvature. Our results are also illuminating to the study of the static screening and the RKKY interaction of the isotropic or anisotropic 3D Dirac/Weyl semimetals or the 2D transition metal dichalcogenide family.

THE GLOBAL CAUCHY PROBLEM FOR THE NLS WITH HIGHER ORDER ANISOTROPIC DISPERSION

We use a method developed by Strauss to obtain global well-posedness results in the mild sense and existence of asymptotic states for the small data Cauchy problem in modulation spaces ${M}^s_{p,q}(\mathbb{R}^d)$, where q = 1 and $s\geq0$ or $q\in(1,\infty]$ and $s>\frac{d}{q'}$ for a nonlinear Schrödinger equation with higher order anisotropic dispersion and algebraic nonlinearities.

Discussing the first velocity dispersion profile of an ultra-diffuse galaxy in MOND

Using Jeans modeling, we calculated the velocity dispersion profile of the ultra-diffuse galaxy (UDG) Dragonfly 44 in MOND. For the nominal mass-to-light ratio from the literature and an isotropic profile, the agreement with the data is excellent near the center of the galaxy. However, in modified gravity, close to the cluster core, the gravitational environment should bring the galaxy back toward Newtonian behavior. The success of the isolated MOND prediction for the central velocity dispersion could then mean that the galaxy is at a great distance (≫5 Mpc) from the cluster core, as hinted by the fact that nearby UDGs share similar velocities with a dispersion well below that of the cluster itself. There is, however, a 2σ tension in the outer part of the UDG due to an increase in the observed dispersion profile with respect to the flat MOND prediction. This deviation could simply be a measurement error. Other possibilities could be, for a UDG far from the cluster, a higher-than-nominal baryonic mass with a tangentially anisotropic dispersion profile or it could even be a dark baryonic halo. If the UDG is closer to the cluster core, the deviation could be a sign that it is in the process of disruption.