The Quantum Geometric Phase between Orthogonal States

We show that the geometric phase between any two states, including orthogonal states, can be computed and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase change in an infinitesimal loop near an orthogonal state. Also, the Pancharatnam phase change during the passage through an orthogonal state is shown to be either $\pi$ or zero (mod $2\pi$). All the off-diagonal geometric phases can be obtained from the projective geometric phase calculated with our generalized connection

Kinematics of the Broad-line Region of 3C 273 from a Ten-year Reverberation Mapping Campaign

Despite many decades of study, the kinematics of the broad-line region of 3C~273 are still poorly understood. We report a new, high signal-to-noise, reverberation mapping campaign carried out from November 2008 to March 2018 that allows the determination of time lags between emission lines and the variable continuum with high precision. The time lag of variations in H$\beta$ relative to those of the 5100 Angstrom continuum is $146.8_{-12.1}^{+8.3}$ days in the rest frame, which agrees very well with the Paschen-$\alpha$ region measured by the GRAVITY at The Very Large Telescope Interferometer. The time lag of the H$\gamma$ emission line is found to be nearly the same as for H$\beta$. The lag of the Fe II emission is $322.0_{-57.9}^{+55.5}$ days, longer by a factor of $\sim$2 than that of the Balmer lines. The velocity-resolved lag measurements of the H$\beta$ line show a complex structure which can be possibly explained by a rotation-dominated disk with some inflowing radial velocity in the H$\beta$-emitting region. Taking the virial factor of $f_{\rm BLR} = 1.3$, we derive a BH mass of $M_{\bullet} = 4.1_{-0.4}^{+0.3} \times 10^8 M_{\odot}$ and an accretion rate of $9.3\,L_{\rm Edd}\,c^{-2}$ from the H$\beta$ line. The decomposition of its $HST$ images yields a host stellar mass of $M_* = 10^{11.3 \pm 0.7} M_\odot$, and a ratio of $M_{\bullet}/M_*\approx 2.0\times 10^{-3}$ in agreement with the Magorrian relation. In the near future, it is expected to compare the geometrically-thick BLR discovered by the GRAVITY in 3C 273 with its spatially-resolved torus in order to understand the potential connection between the BLR and the torus.Comment: 17 pages, 12 figures, 6 tables, accepted for publication in The Astrophysical Journa

Evidence for Gender-Specific Transcriptional Profiles of Nigral Dopamine Neurons in Parkinson Disease

Epidemiological data suggest that the male gender is one of the risks factors for the development of Parkinson Disease (PD). Also, differences in the clinical manifestation and the course of PD have been observed between males and females. However, little is known about the molecular aspects underlying gender-specificity in PD. To address this issue, we determined the gene expression profiles of male and female dopamine (DA) neurons in sporadic PD.We analyzed Affymetrix-based microarrays on laser microdissected DA neurons from postmortem brains of sporadic PD patients and age-matched controls across genders. Pathway enrichment demonstrated that major cellular pathways involved in PD pathogenesis showed different patterns of deregulation between males and females with more prominent downregulation of genes related to oxidative phosphorylation, apoptosis, synaptic transmission and transmission of nerve impulse in the male population. In addition, we found upregulation of gene products for metabolic processes and mitochondrial energy consumption in the age-matched male control neurons. On the single cell level, selected data validation using quantitative Real-Time (qRT)-PCR was consistent with microarray raw data and supported some of the observations from data analysis.On the molecular level, our results provide evidence that the expression profiles of aged normal and PD midbrain DA neurons are gender-specific. The observed differences in the expression profiles suggest a disease bias of the male gender, which could be in concordance with clinical observations that the male gender represents a risk factor for sporadic PD. Validation of gene expression by qRT-PCR supported the microarray results, but also pointed to several caveats involved in data interpretation

Supermassive Black Holes with High Accretion Rates in Active Galactic Nuclei. III. Detection of Fe II Reverberation in Nine Narrow-Line Seyfert 1 Galaxies

This is the third in a series of papers reporting on a large reverberation-mapping campaign aimed to study the properties of active galactic nuclei (AGNs) with high accretion rates. We present new results on the variability of the optical Fe II emission lines in 10 AGNs observed by the Yunnan Observatory 2.4m telescope during 2012--2013. We detect statistically significant time lags, relative to the AGN continuum, in nine of the sources. This accurate measurement is achieved by using a sophisticated spectral fitting scheme that allows for apparent flux variations of the host galaxy, and several narrow lines, due to the changing observing conditions. Six of the newly detected lags are indistinguishable from the Hbeta lags measured in the same sources. Two are significantly longer and one is slightly shorter. Combining with Fe II lags reported in previous studies, we find a Fe II radius--luminosity relationship similar to the one for Hbeta, although our sample by itself shows no clear correlation. The results support the idea that Fe II emission lines originate in photoionized gas which, for the majority of the newly reported objects, is indistinguishable from the Hbeta-emitting gas. We also present a tentative correlation between the lag and intensity of Fe II and Hbeta and comment on its possible origin.Comment: 14 pages, 10 figures, accepted for publication in The Astrophysical Journa