Quantum Geometric Tensor in PT\mathcal{PT}-Symmetric Quantum Mechanics

A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on system's parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $\mathcal{PT}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, i.e., the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $\mathcal{PT}$-symmetry breaking in $\mathcal{PT}$-symmetric systems.Comment: main text of 5 pages, plus supplementary material of 8 page

Analytic decay width of the Higgs boson to massive bottom quarks at next-to-next-to-leading order in QCD

The Higgs boson decay to a massive bottom quark pair provides the dominant contribution to the Higgs boson width. We present an exact result for such a decay induced by the bottom quark Yukawa coupling with next-to-next-to-leading order (NNLO) QCD corrections. We have adopted the canonical differential equations in the calculation and obtained the result in terms of multiple polylogarithms. We also compute the contribution from the decay to four bottom quarks which consist of complete elliptic integrals or their one-fold integrals. The small bottom quark mass limit coincides with the previous calculation using the large momentum expansion. The threshold expansion exhibits power divergent terms in the bottom quark velocity, which has a structure different from that in $e^+e^-\to t\bar{t}$ but can be reproduced by computing the corresponding Coulomb Green function. The NNLO corrections significantly reduce the uncertainties from both the renormalization scale and the renormalization scheme of the bottom quark Yukawa coupling. Our result can be applied to a heavy scalar decay to a top quark pair.Comment: 29 pages, 11 figure

Giant negative magnetoresistance induced by the chiral anomaly in individual Cd3As2 nanowires

Cd3As2 is a newly booming Dirac semimetal with linear dispersion along all three momentum directions and can be viewed as 3D analog of graphene. As breaking of either time reversal symmetry or spatial inversion symmetry, the Dirac semimetal is believed to transform into Weyl semimetal with exotic chiral anomaly effect, while the experimental evidence of the chiral anomaly is still missing in Cd3As2. Here we report the magneto-transport properties of individual Cd3As2 nanowires. Large negative magnetoresistance (MR) with magnitude of -63% at 60 K and -11% at 300 K are observed when the magnetic field is parallel with the electric field direction, giving the evidence of the chiral magnetic effect in Cd3As2 nanowires. In addition, the critical magnetic field BC, where there is an extremum of the negative MR, increases with increasing temperature. As the first observation of chiral anomaly induced negative MR in Cd3As2 nanowires, it may offer valuable insights for low dimensional physics in Dirac semimetals.Comment: 4 figure

Multiple positive solutions for functional dynamic equations on time scales

AbstractIn this paper, we study the following functional dynamic equation on time scales: {[Φ(uΔ(t))]∇+a(t)f(u(t),u(μ(t)))=0,t∈(0,T)T,u(t)=φ(t),t∈[−r,0)T,u(0)−B0(uΔ(0))=0,uΔ(T)=0, where Φ:R→R is an increasing homeomorphism and a positive homomorphism and Φ(0)=0. By using the well-known Leggett–Williams fixed point theorem, existence criteria for multiple positive solutions are established. An example is also given to illustrate the main results

A γ\gamma-ray Quasi-Periodic modulation in the Blazar PKS 0301−-243?

We report a nominally high-confidence $\gamma$-ray quasi-periodic modulation in the blazar PKS 0301$-$243. For this target, we analyze its \emph{Fermi}-LAT Pass 8 data covering from 2008 August to 2017 May. Two techniques, i.e., the maximum likelihood optimization and the exposure-weighted aperture photometry, are used to build the $\gamma$-ray light curves. Then both the Lomb-Scargle Periodogram and the Weighted Wavelet Z-transform are applied to the light curves to search for period signals. A quasi-periodicity with a period of $2.1\pm0.3$ yr appears at the significance level of $\sim5\sigma$, although it should be noted that this putative quasi-period variability is seen in a data set barely four times longer. We speculate that this $\gamma$-ray quasi-periodic modulation might be evidence of a binary supermassive black hole.Comment: 9 pages, 8 figures; Accepted for publication in Ap