Effective potential analytic continuation calculations of real time quantum correlation functions: Asymmetric systems

We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures. Comparing the EPAC results with the exact results, we find that for an asymmetric anharmonic oscillator the EPAC results are in very good agreement with the exact ones at low temperature, while this agreement becomes worse as the temperature increases. We also show that the EPAC calculation for a certain type of asymmetric potentials can be reduced to that for the corresponding symmetric potentials.Comment: RevTeX4, 13 pages, 9 eps figure

Gravitational wave quasinormal mode from Population III massive black hole binaries in various models of population synthesis

Focusing on the remnant black holes after merging binary black holes, we show that ringdown gravitational waves of Population III binary black holes mergers can be detected with the rate of $5.9-500~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for various parameters and functions. This rate is estimated for the events with SNR$>8$ for the second generation gravitational wave detectors such as KAGRA. Here, ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Population III star formation rate and the fraction of binaries, respectively. When we consider only the events with SNR$>35$, the event rate becomes $0.046-4.21~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$. This suggest that for remnant black hole's spin $q_f>0.95$ we have the event rate with SNR$>35$ less than $0.037~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$, while it is $3-30~{\rm events~yr^{-1}}~({\rm SFR_p}/ (10^{-2.5}~M_\odot~{\rm yr^{-1}~Mpc^{-3}})) \cdot ({\rm [f_b/(1+f_b)]/0.33})$ for the third generation detectors such as Einstein Telescope. If we detect many Population III binary black holes merger, it may be possible to constrain the Population III binary evolution paths not only by the mass distribution but also by the spin distribution.Comment: Submitted to PTEP. comments welcom

Possible confirmation of the existence of ergoregion by the Kerr quasinormal mode in gravitational waves from Pop III massive black hole binary

The existence of the ergoregion of the Kerr space-time has not been confirmed observationally yet. We show that the confirmation would be possible by observing the quasinormal mode in gravitational waves. As an example, using the recent population synthesis results of Pop III binary black holes, we find that the peak of the final merger mass ($M_f$) is about $50~\rm M_{\odot}$, while the fraction of the final spin $q_f = a_f/M_f > 0.7$ needed for the confirmation of a part of ergoregion is $\sim 77\%$. To confirm the frequency of the quasinormal mode, ${\rm SNR} > 35$ is needed. The standard model of Pop III population synthesis tells us that the event rate for the confirmation of more than $50\%$ of the ergoregion by the second generation gravitational wave detectors is $\sim 2.3$ ${\rm events\ yr^{-1}\ (SFR_p/(10^{-2.5}\ M_\odot yr^{-1}\ Mpc^{-3}))} \cdot (\rm [f_b/(1+f_b)]/0.33)$ where ${\rm SFR_p}$ and ${\rm f_b}$ are the peak value of the Pop III star formation rate and the fraction of binaries, respectively.Comment: Accepted for publication in PTEP. Comments welcom

Isotropization of Quaternion-Neural-Network-Based PolSAR Adaptive Land Classification in Poincare-Sphere Parameter Space

Quaternion neural networks (QNNs) achieve high accuracy in polarimetric synthetic aperture radar classification for various observation data by working in Poincare-sphere-parameter space. The high performance arises from the good generalization characteristics realized by a QNN as 3-D rotation as well as amplification/attenuation, which is in good consistency with the isotropy in the polarization-state representation it deals with. However, there are still two anisotropic factors so far which lead to a classification capability degraded from its ideal performance. In this letter, we propose an isotropic variation vector and an isotropic activation function to improve the classification ability. Experiments demonstrate the enhancement of the QNN ability