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In this paper, we studied the electromagnetic wave scattered by a time reversal symmetry broken topological insulator circular cylinder. According to the constitutive relations of topological insulator and Maxwell's equation, we derived the scattered electromagnetic fields and scattered coefficients. Numerical results show that the scattered width of the time reversal symmetry topological insulator circular cylinder is extraordinarily different from the width produced by the time reversal symmetry broken topological insulator.

The ground state properties namely the binding energy, the root mean square (rms) radius (neutron, proton and charge) and the deformation parameter of 45 newly identified neutron-rich isotopes in the A~71–152 mass region have been predicted in the relativistic mean filed (RMF) framework along with the Bardeen–Cooper–Schrieffer (BCS) type of pairing. Validity of the RMF results with the NL3 effective force are tested for odd-A Zn and Rh isotopic chains without taking the time reversal symmetry breaking effects into consideration. The RMF prediction on the binding energies are in good agreement with the empirical/finite-range droplet model calculation. The shell effects on the rms radii of odd-A Zn and Rh isotopes are nicely reproduced. The possibility of shape-coexistence in the newly identified nuclei is discussed.

We develop a complex fermionic field-based method to model the properties of the filled bands of topological two-dimensional (2D) matter with time reversal (TR)-symmetry. Using this fermionic representation, we give an explicit calculation of the ${\mathbb{Z}}_2$ index for 2D topological matter invariant under TR and comment on the emergence of Majorana states at the TR-fix points. Moreover, motivated by recent theoretical results on possible signatures of topological supersymmetric matter, we also give the supersymmetric generalization of our TR-invariant construction and calculate the underlying topological ${\mathbb{Z}}_2$ index. Other features such as the topological obstruction of basis sections in the fermionic determinant bundle are also investigated. Applications for the calculations of the supersymmetric charge ${\widehat{Q}}_{\mathrm{\text{susy}}}$ operator and the super-Hamiltonian ${Ĥ}_{\text{susy}}$ for the three-dimensional topological class AII are undertaken; these operators are given by Eqs. (5.48)–(5.51).

Quantum graphs are widely used to investigate properties of quantum chaos. Experimentally, quantum graphs are simulated by microwave graphs (networks) consisting of joints, microwave cables and other microwave components such as attenuators and circulators. This is possible due to an equivalency of the one-dimensional Schrödinger equation describing a quantum system and the telegraph equation describing an ideal microwave network. We present the results of the experimental study of the enhancement factor W_s,β for irregular fully connected hexagon undirected and directed microwave graphs in the presence of absorption. We measured the two-port scattering matrix Ŝ for the undirected microwave graphs which statistical properties of eigenfrequencies, typical for the systems with time reversal symmetry (TRS), can be described by Gaussian Orthogonal Ensemble (GOE) in Random Matrix Theory (RMT), and for the directed graphs possessing the properties of the systems with broken time reversal symmetry, which can be described by Gaussian Unitary Ensemble (GUE) in RMT. The measurements were performed as a function of absorption, which was varied by microwave attenuators.