Reexploration of interacting holographic dark energy model: Cases of interaction term excluding the Hubble parameter

In this paper, we make a deep analysis for the five typical interacting holographic dark energy models with the interaction terms $Q=3\beta H_{0}\rho_{\rm{de}}$, $Q=3\beta H_{0}\rho_{\rm{c}}$, $Q=3\beta H_{0}(\rho_{\rm{de}}+\rho_{\rm c})$, $Q=3\beta H_{0}\sqrt{\rho_{\rm{de}}\rho_{\rm c}}$, and $Q=3\beta H_{0}\frac{\rho_{\rm{de}}\rho_{c}}{\rho_{\rm{de}}+\rho_{\rm c}}$, respectively. We obtain observational constraints on these models by using the type Ia supernova data (the Joint Light-curve Analysis sample), the cosmic microwave background data (Planck 2015 distance priors), the baryon acoustic oscillations data, and the direct measurement of the Hubble constant. We find that the values of $\chi_{\rm min}^2$ for all the five models are almost equal (around~699), indicating that the current observational data equally favor these IHDE models. In addition, a comparison with the cases of interaction term involving the Hubble parameter $H$ is also made.Comment: 14 pages, 6 figures. arXiv admin note: text overlap with arXiv:1710.0306

Thermal entanglement in a two-spin-qutrit system under a nonuniform external magnetic field

The thermal entanglement in a two-spin-qutrit system with two spins coupled by exchange interaction under a magnetic field in an arbitrary direction is investigated. Negativity, the measurement of entanglement, is calculated. We find that for any temperature the evolvement of negativity is symmetric with respect to magnetic field. The behavior of negativity is presented for four different cases. The results show that for different temperature, different magnetic field give maximum entanglement. Both the parallel and antiparallel magnetic field cases are investigated qualitatively (not quantitatively) in detail, we find that the entanglement may be enhanced under an antiparallel magnetic field.Comment: 2 eps figure