Quantifying the entanglement of quantum states under the geometry method

Quantifying entanglement is an important issue in quantum information theory. A straightforward method to quantify entanglement is to measure the distance between the entangled state and the separable sets under the fidelity, distance norm and so on. However, there are few results on the entanglement measure in terms of trace norm. Here we consider the entanglement measures through the trace norm in terms of three methods, the standard measure, the modified measure and the way proposed in [Phys. Rev. A 102. 062401 (2020)]. Specifically, we present some properties of the entanglement measures under the three methods. We also present the analytical expressions for a class of mixed states on two-qubit systems for the standard measure, the pure states for the modified measure and the mixed states on two-qubit systems for the method generated under the third way. And we also generalize the bipartite entanglement measure to a measure for the tripartite states

Dirac-boson stars

In this paper, we construct \textit{Dirac-boson stars} (DBSs) model composed of a scalar field and two Dirac fields. The scalar field and both Dirac fields are in the ground state. We consider the solution families of the DBSs for the synchronized frequency $\tilde{\omega}$ and the nonsynchronized frequency $\tilde{\omega}_D$ cases, respectively. We find several different solutions when the Dirac mass $\tilde{\mu}_D$ and scalar field frequency $\tilde{\omega}_S$ are taken in some particular ranges. In contrast, no similar case has been found in previous studies of multistate boson stars. Moreover, we discuss the characteristics of each type of solution family of the DBSs and present the relationship between the ADM mass $M$ of the DBSs and the synchronized frequency $\tilde{\omega}$ or the nonsynchronized frequency $\tilde{\omega}_D$. Finally, we calculate the binding energy $E_B$ of the DBSs and investigate the relationship of $E_B$ with the synchronized frequency $\tilde{\omega}$ or the nonsynchronized frequency $\tilde{\omega}_D$.Comment: 26 pages, 12 figure

Tidal Love numbers of Axion stars

We investigate the tidal deformability of spherically symmetric axion stars on the stable branches, including the Newtonian and relativistic branches. The results suggest that on the stable branch, the electric Love numbers of axion star are positive, while the magnetic Love numbers are negative. On the Newtonian stable branch, the electric tidal Love numbers are much larger than the magnetic ones, while on the relativistic stable branch, they are slightly larger. Furthermore, the relativistic stable branch has much smaller tidal Love numbers than the Newtonian stable branch, indicating weaker deformability of axion stars on the relativistic stable branch. This could be attributed to the fact that on the relativistic branch, axion stars are more compact, resulting hardly distorted by tidal forces.Comment: 22 pages, 5 figure

Excited Dirac stars with higher azimuthal harmonic index

In this paper, we investigate the properties of the first excited state Dirac stars (DSs) with higher azimuthal harmonic index (specifically, the azimuthal harmonic indexes $m_D$ = $3/2$, $5/2$, $7/2$), as well as the relationship between the ADM mass and angular momentum of Dirac stars with respect to frequency. Moreover, We find that the ergospheres of DSs appear at lower spinor field frequencies, and both the ergospheres and the distribution of the spinor field functions are asymmetric about the equatorial plane. Furthermore, we introduce the ground state scalar field and examine its impact on this system, which is known as the multi-state Dirac-boson stars (DBSs) model. We show various types of solution families for DBSs under both synchronized frequency $\omega$ and nonsynchronized frequencies and find that similar to DSs, the spinor field and the ergospheres of DBSs are also asymmetric about the equatorial plane, but the ergospheres appear at higher spinor field frequencies.Comment: 22 pages, 8 figure

Vibration Analysis of Twin-Screw Compressors Under Partial Load Design: A Case Study

In the practical operation, twin-screw refrigerant compressors may suffer the partial load for a longer period than the full load, while different working condition leads to different response of noise and vibration on the compressor. In this paper, a new approach has been proposed to assess the vibration of a twin-screw refrigeration compressor under 25%, 50%, 75% and 100% load conditions. A powerful computational fluid dynamic (CFD) software, CFX, coupled with a professional grids generation software, TwinMesh, has been used to simulate the rotor loads and p-V indicator diagram which are then checked by the compressor manufacturer’s machine type selection program. Next, the gas-induced loads are applied in a rotor-bearing system established based on the multi-body dynamics for the purpose to assess the vibration signal and give some conclusions for different signal features