Electromagnetic fields, size, and copy of a single photon

Photons are almost involved in each field of science and daily life of everyone. However, there are still some fundamental and puzzling questions such as what a photon is.The expressions of electromagnetic fields of a photon are here proposed. On the basis of the present expressions, we calculate the energy, momentum, and spin angular momentum of a photon, derive the relations between the photon size and wavelength, and reveal the differences between a photon and its copy. The results show that the present expressions properly describe the particle characteristics of a photon; the length of a photon is half of the wavelength, and the radius is proportional to square root of the wavelength; a photon can ionize a hydrogen atom at the ground state only if its radius is less than the Bohr radius; a photon and its copy have the phase difference of {\pi} and constitute a phase-entangled photon pair; the phase-entangled n-photon train results from the sequential stimulated emissions and belongs to the Fock state. A laser beam is an ensemble of the n-photon trains and belongs to the coherent state. The threshold power of a laser is equal to the power of the n-photon train. These provide a bridge between the wave theory of light and quantum optics and will further advance research and application of the related fields.Comment: 4 pages, crrected typos, improved some descriptions and reference

Interference and wave-particle duality of single photons

The wave-particle duality has been said to contain the entire mystery of quantum mechanics. Many delayed-choice experiments have been performed to further understand the wave-particle duality. Here, we reveal some flaws in the known interference theories by comparing the theoretical predictions with the experimental facts and show that the presence of media is a necessary condition for interference of single photons, a photon interferes with other photon via microscopic particles in the interface of media, and the wave-like property of a photon originates from interaction between the photon and media; the particle property is the inherent characteristic of a photon, and the wave-like behavior of a photon always accompanies the particle behavior; the coherent time of single photons cannot be longer than the lifetime of the polarized states of the microscopic particles. Interference of single photons is interpreted properly, and the conundrum of the wave-particle duality is well solved.Comment: 4 pages, 2 figures, 19 references. Corrected typos, added references and arguments, and some descriptions are improve

Constraints on Cardassian universe from Gamma ray bursts

Constraints on the original Cardassian model and the modified polytropic Cardassian model are examined from the recently derived 42 gamma-ray bursts (GRBs) data calibrated with the method avoiding the circularity problem. The results show that GRBs can be an optional observation to constrain on the Cardassian models. Combining the GRBs data with the newly derived size of baryonic acoustic oscillation peak from the Sloan Digital Sky Survey (SDSS), and the position of first acoustic peak of the Cosmic Microwave Background radiation (CMB) from Wilkinson Microwave Anisotropy Probe (WMAP), we find $\Omega_{m0}=0.27_{-0.02}^{+0.02}, n=0.06_{-0.08}^{+0.07}$ ($1\sigma$) for the original Cardassian model, and $\Omega_{m0}=0.27^{+0.03}_{-0.02}$, $n=-0.09_{-1.91}^{+0.23}, \beta=0.82_{-0.62}^{+2.10}$ ($1\sigma$) for the modified polytropic Cardassian model.Comment: 11 pages, 4 figures, accepted for publication in Science in China

Discovery of γ\gamma-ray emission from the radio-intermediate quasar III Zw 2: violent jet activity with intraday γ\gamma-ray variability

III Zw 2 is the prototype of radio-intermediate quasars. Although there is the evidence of possessing strong jet, significant $\gamma$-ray emission has not been reported before. In this work, we carry out a detailed analysis of the latest {\it Fermi}-LAT {\it Pass} 8 data. No significant $\gamma$-ray signal has been detected in the time-averaged 7-year {\it Fermi}-LAT data of III Zw 2, we however have identified two distinct $\gamma$-ray flares with isotropic luminosities of $\sim 10^{45}$ erg $\rm s^{-1}$. Multiwavelength data analysis (including also the optical photometric observations from Yunnan Observatories) are presented and the main finding is the simultaneous optical and $\gamma$-ray flares of III Zw 2 appearing in Nov. 2009. Violent $\gamma$-ray variability with doubling timescale of 2.5 hours was detected in another $\gamma$-ray flare in May 2010, for which the 3-hour $\gamma$-ray peak flux is $\sim 250$ times of the average flux in 7 years. Rather similar behaviors are observed in blazars and the blazar model can reasonably reproduce the spectral energy distribution of III Zw 2 in a wide energy range, strongly suggesting that its central engine resembles that of blazars. In view of its core which shares radio similarities with young radio sources together with the weak extended radio lobe emission, we suggest that III Zw 2 harbors a recurrent activity core and serves as a valuable target for investigating the fuelling and triggering of the activity in radio loud AGNs.Comment: ApJS in press, welcome any comment

Neutral Higgs production on LHC in the two-Higgs-doublet model with spontaneous CPCP violation

Spontaneous CP violation motivates the introduction of two Higgs doublets in the electroweak theory, such a simple extension of the standard model has five physical Higgs bosons and rich CP-violating sources. Exploration on more than one Higgs boson is a direct evidence for new physics beyond the standard model. The neutral Higgs production at LHC is investigated in such a general two Higgs doublet model with spontaneous CP violation, it is shown that the production cross section and decays of the neutral Higgs boson can significantly be different from the predictions from the standard model.Comment: 15 pages, 12 figures, published version in PR

The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory

In this work, for a finite group $G$ and a 4-cocycle $\omega \in Z^4(G, \mathbf{k}^\times)$, we compute explicitly the center of the monoidal 2-category $\operatorname{2Vec}_G^{\omega}$ of $\omega$-twisted $G$-graded 1-categories of finite dimensional $\mathbf{k}$-vector spaces. This center gives a precise mathematical description of the topological defects in the associated 3+1D Dijkgraaf-Witten TQFT. We prove that this center is a braided monoidal 2-category with a trivial sylleptic center.Comment: 24 page

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Symmetry plays a fundamental role in physics. The quasi-degeneracy between single-particle orbitals $(n, l, j = l + 1/2)$ and $(n-1, l + 2, j = l + 3/2)$ indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry (PSS). Since the introduction of the concept of PSS in atomic nuclei, there have been comprehensive efforts to understand its origin. Both splittings of spin doublets and pseudospin doublets play critical roles in the evolution of magic numbers in exotic nuclei discovered by modern spectroscopic studies with radioactive ion beam facilities. Since the PSS was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry (SS) for anti-nucleon, and many new concepts have been introduced. In the present Review, we focus on the recent progress on the PSS and SS in various systems and potentials, including extensions of the PSS study from stable to exotic nuclei, from non-confining to confining potentials, from local to non-local potentials, from central to tensor potentials, from bound to resonant states, from nucleon to anti-nucleon spectra, from nucleon to hyperon spectra, and from spherical to deformed nuclei. Open issues in this field are also discussed in detail, including the perturbative nature, the supersymmetric representation with similarity renormalization group, and the puzzle of intruder states.Comment: Review Article, 242 pages, 58 figures, 10 table

Anti-Hyperon polarization in high energy pp collisions with polarized beams

We study the longitudinal polarization of the Sigma_bar and Xi_bar anti-hyperons in polarized high energy pp collisions at large transverse momenta, extending a recent study for the Lambda_bar anti-hyperon. We make predictions by using different parametrizations of the polarized parton densities and models for the polarized fragmentation functions. Similar to the Lambda_bar polarization, the Xi_bar0 and Xi_bar+ polarizations are found to be sensitive to the polarized anti-strange sea in the nucleon. The Sigma_bar- and Sigma_bar+ polarizations show sensitivity to the light sea quark polarizations, \Delta \bar u(x) and \Delta \bar d(x), and their asymmetry.Comment: 17 pages, 9 figures,version to appear in PR

TG-GAN: Continuous-time Temporal Graph Generation with Deep Generative Models

The recent deep generative models for static graphs that are now being actively developed have achieved significant success in areas such as molecule design. However, many real-world problems involve temporal graphs whose topology and attribute values evolve dynamically over time, including important applications such as protein folding, human mobility networks, and social network growth. As yet, deep generative models for temporal graphs are not yet well understood and existing techniques for static graphs are not adequate for temporal graphs since they cannot 1) encode and decode continuously-varying graph topology chronologically, 2) enforce validity via temporal constraints, or 3) ensure efficiency for information-lossless temporal resolution. To address these challenges, we propose a new model, called ``Temporal Graph Generative Adversarial Network'' (TG-GAN) for continuous-time temporal graph generation, by modeling the deep generative process for truncated temporal random walks and their compositions. Specifically, we first propose a novel temporal graph generator that jointly model truncated edge sequences, time budgets, and node attributes, with novel activation functions that enforce temporal validity constraints under recurrent architecture. In addition, a new temporal graph discriminator is proposed, which combines time and node encoding operations over a recurrent architecture to distinguish the generated sequences from the real ones sampled by a newly-developed truncated temporal random walk sampler. Extensive experiments on both synthetic and real-world datasets demonstrate TG-GAN significantly outperforms the comparison methods in efficiency and effectiveness

Acoustic imaging and collimating by slabs of sonic crystals made from arrays of rigid cylinders in air

We show some new properties of the acoustic propagation in two-dimensional sonic crystals, formed by parallel rigid cylinders placed in air. The transmission through slabs of sonic crystals and the associated band structures are considered. It is shown that within partial bandgaps, the waves tend to be collimated or guided into the direction in which the propagation is allowed. Such a feature also prevails in the situations in which deaf bands appear. We show that within the partial bandgaps, a stable imaging effect can be obtained for flat sonic crystal slabs, in analogy to the cases with photonic crystals.Comment: 11 pages, 5 figure