Shadows and photon spheres with spherical accretions in the four-dimensional Gauss-Bonnet black hole

We investigate the shadows and photon spheres of the four-dimensional Gauss-Bonnet black hole with the static and infalling spherical accretions. We show that for both cases, the shadow and photon sphere are always present. The radii of the shadow and photon sphere are independent of the profiles of accretion for a fixed Gauss-Bonnet constant, implying that the shadow is a signature of the spacetime geometry and it is hardly influenced by accretion in this case. Because of the Doppler effect, the shadow of the infalling accretion is found to be darker than that of the static one. We also investigate the effect of the Gauss-Bonnet constant on the shadow and photon sphere, and find that the larger the Gauss-Bonnet constant is, the smaller the radii of the shadow and photon sphere will be. In particular, the observed specific intensity increases with the increasing of the Gauss-Bonnet constant.Comment: published versio

Quantum Geometric Tensor in PT\mathcal{PT}-Symmetric Quantum Mechanics

A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on system's parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $\mathcal{PT}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, i.e., the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $\mathcal{PT}$-symmetry breaking in $\mathcal{PT}$-symmetric systems.Comment: main text of 5 pages, plus supplementary material of 8 page

Linear magnetoconductivity in an intrinsic topological Weyl semimetal

Searching for the signature of the violation of chiral charge conservation in solids has inspired a growing passion on the magneto-transport in topological semimetals. One of the open questions is how the conductivity depends on magnetic fields in a semimetal phase when the Fermi energy crosses the Weyl nodes. Here, we study both the longitudinal and transverse magnetoconductivity of a topological Weyl semimetal near the Weyl nodes with the help of a two-node model that includes all the topological semimetal properties. In the semimetal phase, the Fermi energy crosses only the 0th Landau bands in magnetic fields. For a finite potential range of impurities, it is found that both the longitudinal and transverse magnetoconductivity are positive and linear at the Weyl nodes, leading to an anisotropic and negative magnetoresistivity. The longitudinal magnetoconductivity depends on the potential range of impurities. The longitudinal conductivity remains finite at zero field, even though the density of states vanishes at the Weyl nodes. This work establishes a relation between the linear magnetoconductivity and the intrinsic topological Weyl semimetal phase.Comment: An extended version accepted by New. J. Phys. with 15 pages and 3 figure