Relation Between Gravitational Mass and Baryonic Mass for Non-Rotating and Rapidly Rotating Neutron Stars

With a selected sample of neutron star (NS) equations of state (EOSs) that are consistent with the current observations and have a range of maximum masses, we investigate the relations between NS gravitational mass Mg and baryonic mass Mb, and the relations between the maximum NS mass supported through uniform rotation (Mmax) and that of nonrotating NSs (MTOV). We find that for an EOS-independent quadratic, universal transformation formula (Mb=Mg+A×M2g)(Mb=Mg+A×Mg2), the best-fit A value is 0.080 for non-rotating NSs, 0.064 for maximally rotating NSs, and 0.073 when NSs with arbitrary rotation are considered. The residual error of the transformation is ∼ 0.1M⊙ for non-spin or maximum-spin, but is as large as ∼ 0.2M⊙ for all spins. For different EOSs, we find that the parameter A for non-rotating NSs is proportional to R−11.4R1.4−1 (where R1.4 is NS radius for 1.4M⊙ in units of km). For a particular EOS, if one adopts the best-fit parameters for different spin periods, the residual error of the transformation is smaller, which is of the order of 0.01M⊙ for the quadratic form and less than 0.01M⊙ for the cubic form ((Mb=Mg+A1×M2g+A2×M3g)(Mb=Mg+A1×Mg2+A2×Mg3)). We also find a very tight and general correlation between the normalized mass gain due to spin Δm = (Mmax − MTOV)/MTOV and the spin period normalized to the Keplerian period PP, i.e., log10Δm=(−2.74±0.05)log10P+log10(0.20±0.01)log10Δm=(−2.74±0.05)log10P+log10(0.20±0.01), which is independent of EOS models. These empirical relations are helpful to study NS-NS mergers with a long-lived NS merger product using multi-messenger data. The application of our results to GW170817 is discussed

Observation of optical vortices in momentum space

Vortex, the winding of a vector field in two dimensions, has its core the field singularity and its topological charge defined by the quantized winding angle of the vector field. Vortices are one of the most fundamental topological excitations in nature, widely known in hair whorls as the winding of hair strings, in fluid dynamics as the winding of velocities, in angular-momentum beams as the winding of phase angle and in superconductors and superfluids as the winding of order parameters. Nevertheless, vortices have hardly been observed other than those in the real space. Although band degeneracies, such as Dirac cones, can be viewed as momentum-space vortices in their mathematical structures, there lacks a well-defined physical observable whose winding number is an arbitrary signed integer. Here, we experimentally observed momentum-space vortices as the winding of far-field polarization vectors in the Brillouin zone (BZ) of periodic plasmonic structures. Using a home-made polarization-resolved momentum-space imaging spectroscopy, we completely map out the dispersion, lifetime and polarization of all radiative states at the visible wavelengths. The momentum space vortices were experimentally identified by their winding patterns in the polarization-resolved iso-frequency contours and their diverging radiative quality factors. Such polarization vortices can exist robustly on any periodic systems of vectorial fields, while they are not captured by the existing topological band theory developed for scaler fields. This work opens up a promising avenue for exploring topological photonics in the momentum space, studying bound states in continuum (BICs), as well as for rendering and steering vector beams and designing high-Q plasmonic resonances.Comment: 7 pages, 4 figure

A Novel Multifunction Digital Chip Design Based on CMOS Technology

The realization of an analog-to-digital-conversion chip has great significance in the applications of electronic products. By considering mature time–number digitization, a new multifunction digital chip with a long time delay was designed in this study on the basis of the principle of analog-to-time conversion (ATC) and the realization of long time delay. With additional resistance, capacitance, and transistors, this chip can easily realize ATC, monostable triggers, Schmitt triggers, and multivibrators. The circuit composition of this chip was analyzed, and every module design was introduced. According to the simulation result of Hspice and CSMC 2P2M CMOS (Complementary Metal Oxide Semiconductor) process database, the chip layout (1mm2) design was accomplished by using CSMC 2P2M CMOS technology. Finally, the designed chip was applied in multiproject wafer flow. The flow test demonstrated that this new chip can meet design goal and is applicable to various digital integrated chip designs as an IP (intellectual property) core

Red-QAOA: Efficient Variational Optimization through Circuit Reduction

The Quantum Approximate Optimization Algorithm (QAOA) addresses combinatorial optimization challenges by converting inputs to graphs. However, the optimal parameter searching process of QAOA is greatly affected by noise. Larger problems yield bigger graphs, requiring more qubits and making their outcomes highly noise-sensitive. This paper introduces Red-QAOA, leveraging energy landscape concentration via a simulated annealing-based graph reduction. Red-QAOA creates a smaller (distilled) graph with nearly identical parameters to the original graph. The distilled graph produces a smaller quantum circuit and thus reduces noise impact. At the end of the optimization, Red-QAOA employs the parameters from the distilled graph on the original graph and continues the parameter search on the original graph. Red-QAOA outperforms state-of-the-art Graph Neural Network (GNN)-based pooling techniques on 3200 real-world problems. Red-QAOA reduced node and edge counts by 28% and 37%, respectively, with a mean square error of only 2%

A Solvable Model for Discrete Time Crystal Enforced by Nonsymmorphic Dynamical Symmetry

Discrete time crystal is a class of nonequilibrium quantum systems exhibiting subharmonic responses to external periodic driving. Here we propose a class of discrete time crystals enforced by nonsymmorphic dynamical symmetry. We start with a system with nonsymmorphic dynamical symmetry, in which the instantaneous eigenstates become M\"obius twisted, hence doubling the period of the instantaneous state. The exact solution of the time-dependent Schr\"odinger equation shows that the system spontaneously exhibits a period extension without undergoing quantum superposition states for a series of specifc evolution frequencies or in the limit of long evolution period. Moreover, in such case the system gains a {\pi} Berry phase after two periods' evolution. Finally, we show that the subharmonic response is stable even when many-body interactions are introduced, indicating a DTC phase in the thermodynamic limit.Comment: 5 pages, 4 figure