Shadow thermodynamics of the Hayward-AdS black hole

In this paper, the phase structure of the Hayward-AdS black hole (BH) is studied using shadow formalism. It has been found that the shadow radius is a monotonic function of the horizon radius and can therefore play an equivalent role to the horizon radius in characterizing the thermodynamics of Hayward-AdS BH. The thermodynamic phase transition (PT) of the Hayward-AdS BH is investigated with the shadow radius. It is shown that as the magnetic charge increases, the shadow radius becomes larger, while the coexistence temperature becomes lower. The thermal profile of the Hayward-AdS BH is established by combining the temperature diagram and the shadow cast diagram, which shows that for a fixed magnetic charge, the temperature of the Hayward-AdS BH increases with the pressure while the region of the thermal profile decreases with the pressure. In particular, the temperature of the Hayward-AdS BH follows an N-type change trend when it is smaller than the critical temperature. This imply that the BH shadow may be used to investigate the thermodynamics of the Hayward-AdS BH.Comment: 14 pages, 6 figure

A sharp version of Kahan's theorem on clustered eigenvalues

AbstractLet the n × n Hermitian matrix A have eigenvalues λ1, λ2, …, λn, let the k × k Hermitian matrix H have eigenvalues μ1 ≤ μ2 … ≤ μk, and let Q be an n × k matrix having full column rank, so 1 ≤ k ≤ n. It is proved that there exist k eigenvalues λi1 ≤ λi2 ≤ … ≤ λik of A such thatmax1≤j≤k|μj − λij| ≤ Cσmin(Q) ‖AQ − QH‖2always holds with c = 1, where σmin (Q) is the smallest singular value of Q, and ‖; · ‖;2 denotes the biggest singular value of a matrix. The inequality was proved for c ≤ √2 in 1967 by Kahan, who also conjectured that it should be true for c = 1

Estimating Power Spectrum of Sunyaev-Zeldovich Effect from the Cross-Correlation between WMAP and 2MASS

We estimate the power spectrum of SZ(Sunyaev-Zel'dovich)-effect-induced temperature fluctuations on sub-degree scales by using the cross correlation between the three-year WMAP maps and 2MASS galaxy distribution. We produced the SZ effect maps by hydrodynamic simulation samples of the $\Lambda$CDM model, and show that the SZ effect temperature fluctuations are highly non-Gaussian. The PDF of the temperature fluctuations has a long tail. More than 70% power of the SZ effect temperature fluctuations attributes to top $\sim 1$ wavelet modes (long tail events). On the other hand, the CMB temperature fluctuations basically are Gaussian. Although the mean power of CMB temperature fluctuations on sub-degree scales is much higher than that of SZ effect map, the SZ effect temperature fluctuations associated with top 2MASS clusters is comparable to the power of CMB temperature fluctuations on the same scales. Thus, from noisy WMAP maps, one can have a proper estimation of the SZ effect power at the positions of the top 2MASS clusters. The power spectrum given by these top wavelet modes is useful to constrain the parameter of density fluctuations amplitude $\sigma_8$. We find that the power spectrum of these top wavelet modes of SZ effect on sub-degree scales basically is consistent with the simulation maps produced with $\sigma_8=0.84$. The simulation samples of $\sigma_8=0.74$ show, however, significant deviation from detected SZ power spectrum. It can be ruled out with confidence level 99% if all other cosmological parameters are the same as that given by the three-year WMAP results.Comment: 26 pages, 10 figures, accepted for publication in Ap

A possible subthreshold pole in S11S_{11} channel from πN\pi N Roy-Steiner equation analyses

The hyperbolic version of Roy-Steiner equation describing low energy $\pi N$ scatterings, with larger analyticity domain in the complex $s$ plane is solved. The numerical results on phase shifts of low partial waves are in agreement with that of Hoferichter et al. [Phys. Rept. 625 (2016) 1]. A subthreshold pole in $S_{11}$ channel is found located at $\sqrt{s}=(918 \pm 3)-i (163 \pm 9)$~MeV.Comment: 12 pages, 4 figures; Minor improvements in numerical results and discussions, conclusions unchanged, final version to appear in JHE

A New ZrCuSiAs-Type Superconductor: ThFeAsN

We report the first nitrogen-containing iron-pnictide superconductor ThFeAsN, which is synthesized by a solid-state reaction in an evacuated container. The compound crystallizes in a ZrCuSiAs-type structure with the space group P4/nmm and lattice parameters a=4.0367(1) {\AA} and c=8.5262(2) {\AA} at 300 K. The electrical resistivity and dc magnetic susceptibility measurements indicate superconductivity at 30 K for the nominally undoped ThFeAsN.Comment: 6 pages, 4 figures, 1 tabl