Multi-dimensional band structure spectroscopy in the synthetic frequency dimension

The concept of synthetic dimensions in photonics provides a versatile platform in exploring multi-dimensional physics. Many of these physics are characterized by band structures in more than one dimensions. Existing efforts on band structure measurements in the photonic synthetic frequency dimension however are limited to either one-dimensional Brillouin zones or one-dimensional subsets of multi-dimensional Brillouin zones. Here we theoretically propose and experimentally demonstrate a method to fully measure multi-dimensional band structures in the synthetic frequency dimension. We use a single photonic resonator under dynamical modulation to create a multi-dimensional synthetic frequency lattice. We show that the band structure of such a lattice over the entire multi-dimensional Brillouin zone can be measured by introducing a gauge potential into the lattice Hamiltonian. Using this method, we perform experimental measurements of two-dimensional band structures of a Hermitian and a non-Hermitian Hamiltonian. The measurements reveal some of the general properties of point-gap topology of the non-Hermitian Hamiltonian in more than one dimensions. Our results demonstrate experimental capabilities to fully characterize high-dimensional physical phenomena in the photonic synthetic frequency dimension

Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. IV. Hβ\beta Time Lags and Implications for Super-Eddington Accretion

We have completed two years of photometric and spectroscopic monitoring of a large number of active galactic nuclei (AGNs) with very high accretion rates. In this paper, we report on the result of the second phase of the campaign, during 2013--2014, and the measurements of five new H$\beta$ time lags out of eight monitored AGNs. All five objects were identified as super-Eddington accreting massive black holes (SEAMBHs). The highest measured accretion rates for the objects in this campaign are $\dot{\mathscr{M}}\gtrsim 200$, where $\dot{\mathscr{M}}= \dot{M}_{\bullet}/L_{\rm Edd}c^{-2}$, $\dot{M}_{\bullet}$ is the mass accretion rates, $L_{\rm Edd}$ is the Eddington luminosity and $c$ is the speed of light. We find that the H$\beta$ time lags in SEAMBHs are significantly shorter than those measured in sub-Eddington AGNs, and the deviations increase with increasing accretion rates. Thus, the relationship between broad-line region size ($R_{_{\rm H\beta}}$) and optical luminosity at 5100\AA, $R_{_{\rm H\beta}}-L_{5100}$, requires accretion rate as an additional parameter. We propose that much of the effect may be due to the strong anisotropy of the emitted slim-disk radiation. Scaling $R_{_{\rm H\beta}}$ by the gravitational radius of the black hole, we define a new radius-mass parameter ($Y$) and show that it saturates at a critical accretion rate of $\dot{\mathscr{M}}_c=6\sim 30$, indicating a transition from thin to slim accretion disk and a saturated luminosity of the slim disks. The parameter $Y$ is a very useful probe for understanding the various types of accretion onto massive black holes. We briefly comment on implications to the general population of super-Eddington AGNs in the universe and applications to cosmology.Comment: 53 pages, 12 figures, 7 tables, accepted for publication in The Astrophysical Journa

Influence of macroeconomics factors and legal stability to the insurance growth in the ASEAN-5 countries

This paper examines the influence of legal stability and macroeconomics factor to the non-life insurance development. In light of the growing significance of foreign direct investment (FDI) and trade that stimulate insurance sector, and the stress placed on legal stability of the countries, investigating the role of legal stability is crucial to sustain a country’s financial development. This study employs a panel data analysis spanning 20 years in the selected developing countries. The findings suggest that higher trade, higher income, higher stock market trading activities and higher availability of finance credit will enhance the non-life insurance development. Legal stability such as enhancement on the property right and government integrity will improve the non-life insurance development. When the legal environments in emerging countries are more stable, the FDI and stocks market will become more encouraging and stimulate non-life insurance development. The policy makers should improve the legal stability in emerging countries to improve the financial development for minimizing the gap with developed countries. This study includes the institutional factors components in addition to the macroeconomics factors could provide a complete picture towards the improvement of non-life insurance development in emerging and transition countries