Systematic study of the symmetry energy coefficient in finite nuclei

The symmetry energy coefficients in finite nuclei have been studied systematically with a covariant density functional theory (DFT) and compared with the values calculated using several available mass tables. Due to the contamination of shell effect, the nuclear symmetry energy coefficients extracted from the binding energies have large fluctuations around the nuclei with double magic numbers. The size of this contamination is shown to be smaller for the nuclei with larger isospin value. After subtracting the shell effect with the Strutinsky method, the obtained nuclear symmetry energy coefficients with different isospin values are shown to decrease smoothly with the mass number $A$ and are subsequently fitted to the relation $\dfrac{4a_{\rm sym}}{A}=\dfrac{b_v}{A}-\dfrac{b_s}{A^{4/3}}$. The resultant volume $b_v$ and surface $b_s$ coefficients from axially deformed covariant DFT calculations are $121.73$ and $197.98$ MeV respectively. The ratio $b_s/b_v=1.63$ is in good agreement with the value derived from the previous calculations with the non-relativistic Skyrme energy functionals. The coefficients $b_v$ and $b_s$ corresponding to several available mass tables are also extracted. It is shown that there is a strong linear correlation between the volume $b_v$ and surface $b_s$ coefficients and the ratios $b_s/b_v$ are in between $1.6-2.0$ for all the cases.Comment: 16 pages, 6 figure

Gapped spin liquid with Z2\mathbb{Z}_2-topological order for kagome Heisenberg model

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. We also introduce a very sensitive probe for the gap of the ground state -- the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of Heisenberg model on Kagome lattice is a gapped spin liquid with the $\mathbb{Z}_2$-topological order (or toric code type), which has a long correlation length $\xi\sim 10$ unit cell length. We justify that the TRG method can handle very large systems with over thousands of spins. Such a long $\xi$ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than 10 unit cell length. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.Comment: 10 pages, 7 figure

Temporal Deformable Convolutional Encoder-Decoder Networks for Video Captioning

It is well believed that video captioning is a fundamental but challenging task in both computer vision and artificial intelligence fields. The prevalent approach is to map an input video to a variable-length output sentence in a sequence to sequence manner via Recurrent Neural Network (RNN). Nevertheless, the training of RNN still suffers to some degree from vanishing/exploding gradient problem, making the optimization difficult. Moreover, the inherently recurrent dependency in RNN prevents parallelization within a sequence during training and therefore limits the computations. In this paper, we present a novel design --- Temporal Deformable Convolutional Encoder-Decoder Networks (dubbed as TDConvED) that fully employ convolutions in both encoder and decoder networks for video captioning. Technically, we exploit convolutional block structures that compute intermediate states of a fixed number of inputs and stack several blocks to capture long-term relationships. The structure in encoder is further equipped with temporal deformable convolution to enable free-form deformation of temporal sampling. Our model also capitalizes on temporal attention mechanism for sentence generation. Extensive experiments are conducted on both MSVD and MSR-VTT video captioning datasets, and superior results are reported when comparing to conventional RNN-based encoder-decoder techniques. More remarkably, TDConvED increases CIDEr-D performance from 58.8% to 67.2% on MSVD.Comment: AAAI 201

Commanding Wheelchair in Virtual Reality with Thoughts by Multiclass BCI based on Movement-related Cortical Potentials

Brain-driven wheelchair control is an attractive application in theBrain-Computer Interface (BCI) field. In this research, wedesigned and validated a virtual wheelchair navigation systemcontrolled by our latest multiclass BCI Menu interface based on afast brain switch, which provides five commands: move forward,turn left, turn right, move backward, and stop. Preliminary resultshave shown that subjects can successfully control the wheelchairto hit all targets in the immersive virtual reality (VR)environment. This system proves an avenue to bridge the gapbetween simulation control in VR environments and real-lifewheelchair applications for mobility impairment

Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes

The recently developed structure model that uses the generator coordinate method to perform configuration mixing of angular-momentum projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes (3DAMP+GCM), is applied in a systematic study of ground states and low-energy collective states in the even-even magnesium isotopes $^{20-40}$Mg. Results obtained using a relativistic point-coupling nucleon-nucleon effective interaction in the particle-hole channel, and a density-independent $\delta$-interaction in the pairing channel, are compared to data and with previous axial 1DAMP+GCM calculations, both with a relativistic density functional and the non-relativistic Gogny force. The effects of the inclusion of triaxial degrees of freedom on the low-energy spectra and E2 transitions of magnesium isotopes are examined.Comment: 28 pages, 11 figures and 1 tabl

Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors

Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena, which can be fundamentally traced back to non-unitarity and is much more fundamental and universal than complex energy spectrum. In this paper, we introduce an interesting quantity (denoted as $\eta$) as a new variant of the Petermann factor to directly and efficiently measure non-unitarity and the associated non-Hermitian physics. By tuning the model parameters of underlying non-Hermitian systems, we find that the discontinuity of both $\eta$ and its first-order derivative (denoted as $\partial \eta$) pronouncedly captures rich physics that is fundamentally caused by non-unitarity. More concretely, in the 1D non-Hermitian topological systems, two mutually orthogonal edge states that are respectively localized on two boundaries become non-orthogonal in the vicinity of discontinuity of $\eta$ as a function of the model parameter, which is dubbed ``edge state transition''. Through theoretical analysis, we identify that the appearance of edge state transition indicates the existence of exceptional points~(EPs) in topological edge states. Regarding the discontinuity of $\partial\eta$, we investigate a two-level non-Hermitian model and establish a connection between the points of discontinuity of $\partial \eta$ and EPs of bulk states. By studying this connection in more general lattice models, we find that some models have discontinuity of $\partial\eta$, implying the existence of EPs in bulk states