New features of scattering from a one-dimensional non-Hermitian (complex) potential

For complex one-dimensional potentials, we propose the asymmetry of both reflectivity and transmitivity under time-reversal: $R(-k)\ne R(k)$ and $T(-k) \ne T(k)$, unless the potentials are real or PT-symmetric. For complex PT-symmetric scattering potentials, we propose that $R_{left}(-k)=R_{right}(k)$ and $T(-k)=T(k)$. So far, the spectral singularities (SS) of a one-dimensional non-Hermitian scattering potential are witnessed/conjectured to be at most one. We present a new non-Hermitian parametrization of Scarf II potential to reveal its four new features. Firstly, it displays the just acclaimed (in)variances. Secondly, it can support two spectral singularities at two pre-assigned real energies ($E_*=\alpha^2,\beta^2$) either in $T(k)$ or in $T(-k)$, when $\alpha\beta>0$. Thirdly, when $\alpha \beta <0$ it possesses one SS in $T(k)$ and the other in $T(-k)$. Fourthly, when the potential becomes PT-symmetric $[(\alpha+\beta)=0]$, we get $T(k)=T(-k)$, it possesses a unique SS at $E=\alpha^2$ in both $T(-k)$ and $T(k)$. Lastly, for completeness, when $\alpha=i\gamma$ and $\beta=i\delta$, there are no SS, instead we get two negative energies $-\gamma^2$ and $-\delta^2$ of the complex PT-symmetric Scarf II belonging to the two well-known branches of discrete bound state eigenvalues and no spectral singularity exists in this case. We find them as $E^{+}_{M}=-(\gamma-M)^2$ and $E^{-}_{N}=-(\delta-N)^2$; $M(N)=0,1,2,...$ with $0 \le M (N)< \gamma (\delta)$. {PACS: 03.65.Nk,11.30.Er,42.25.Bs}Comment: 10 pages, one Table, one Figure, important changes, appeared as an FTC (J. Phys. A: Math. Theor. 45(2012) 032004

Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices

Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudo-unitary group. Further, we develop a random matrix theory which is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices as the pseudo-unitary ensemble. We obtain exact results for the nearest-neighbour level spacing distribution for (2 X 2) PT-symmetric Hamiltonian matrices which has a novel form, s log (1/s) near zero spacing. This shows a level repulsion in marked distinction with an algebraic form in the Wigner surmise. We believe that this paves way for a description of varied phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and so on.Comment: 9 pages, 2 figures, LaTeX, submitted to the Physical Review Letters on August 20, 200

Reflectionless Potentials and PT Symmetry

Large families of Hamiltonians that are non-Hermitian in the conventional sense have been found to have all eigenvalues real, a fact attributed to an unbroken PT symmetry. The corresponding quantum theories possess an unconventional scalar product. The eigenvalues are determined by differential equations with boundary conditions imposed in wedges in the complex plane. For a special class of such systems, it is possible to impose the PT-symmetric boundary conditions on the real axis, which lies on the edges of the wedges. The PT-symmetric spectrum can then be obtained by imposing the more transparent requirement that the potential be reflectionless.Comment: 4 Page

Status and diversity of coastal avian fauna in Gwadar peninsula, Balochistan

The 1050 km long coastline of Pakistan, extends from Sir Creek in the southeast of Indus delta to Gwadar Bay in the west. This article is based on diversity, habitat, status and distribution of different species of coastal birds present in the Gwadar coast. Observation of birds was done during winter season at four different sites. The habitat is important for different coastal birds like terns, gulls, pelicans and waders including resident and migratory species. A total of 55 species were recorded from the entire area. The species richness was higher at two sites. The birds were seen in higher numbers at uninhabited points compared to those near the populated area or the port. Shannon diversity index for bird community was calculated for four sites namely Shabi Estuary, Gwadar East Bay, Gwadar West Bay and Gurab, where the diversity was found to be 2.82, 2.27, 2.33 and 2.40 respectively. Birds of Common Sandpiper (Actitishy poleucos), Common Teal (Anas crecca), Wigeon (Anas Penelope), Shoveller (Anas clypeata), Pochard (Aythya ferina), Common Coot (Fulica atra), Grey Plover (Pluvialis squatarola), Kentish Plover (Charadrius alexandriunus), Dusk Red Shank (Tringa erythropus) and Great White Pelicans (Pelecanus onocrotalus) have been recorded in large numbers during the study period. Some vulnerable species for e.g. Pochard (Aythya ferina) and endangered species for e.g. Great Knot (Calidris tenuirostris), Egyptian Vulture (Neophron percnopterus), and two near threatened species Oyster catcher (Haematus ostralegus) and Dalmation Pelican (Pelecanus crispus) were also recorded. The major threats to the ecosystem are habitat degradation due to port construction, urbanization, hunting, poaching and other anthropogenic activities

Number of quantal resonances

Employing the concept of time-delay, a relation is found which counts the number of quantal resonances supported by a potential. Several simple and advanced illustrations include a treatment of square-well, Dirac delta barrier, an interesting physical situation from neutron reflectometry, and the Delta resonance appearing in the scattering of \pi meson from proton.Comment: 9 pages, 5 figure

Study of J/ψJ/\psi and ψ(3686)→Σ(1385)0Σˉ(1385)0\psi(3686)\rightarrow\Sigma(1385)^{0}\bar\Sigma(1385)^{0} and Ξ0Ξˉ0\Xi^0\bar\Xi^{0}

We study the decays of $J/\psi$ and $\psi(3686)$ to the final states $\Sigma(1385)^{0}\bar\Sigma(1385)^{0}$ and $\Xi^0\bar\Xi^{0}$ based on a single baryon tag method using data samples of $(1310.6 \pm 7.0) \times 10^{6}$ $J/\psi$ and $(447.9 \pm 2.9) \times 10^{6}$ $\psi(3686)$ events collected with the BESIII detector at the BEPCII collider. The decays to $\Sigma(1385)^{0}\bar\Sigma(1385)^{0}$ are observed for the first time. The measured branching fractions of $J/\psi$ and $\psi(3686)\rightarrow\Xi^0\bar\Xi^{0}$ are in good agreement with, and much more precise, than the previously published results. The angular parameters for these decays are also measured for the first time. The measured angular decay parameter for $J/\psi\rightarrow\Sigma(1385)^{0}\bar\Sigma(1385)^{0}$, $\alpha =-0.64 \pm 0.03 \pm 0.10$, is found to be negative, different to the other decay processes in this measurement. In addition, the "12\% rule" and isospin symmetry in the $J/\psi$ and $\psi(3686)\rightarrow\Xi\bar\Xi$ and $\Sigma(1385)\bar{\Sigma}(1385)$ systems are tested.Comment: 11 pages, 7 figures. This version is consistent with paper published in Phys.Lett. B770 (2017) 217-22

Observation of Ds+→pnˉD^+_s\rightarrow p\bar{n} and confirmation of its large branching fraction

The baryonic decay $D^+_s\rightarrow p\bar{n}$ is observed, and the corresponding branching fraction is measured to be $(1.21\pm0.10\pm0.05)\times10^{-3}$, where the first uncertainty is statistical and second systematic. The data sample used in this analysis was collected with the BESIII detector operating at the BEPCII $e^+e^-$ double-ring collider with a center-of-mass energy of 4.178~GeV and an integrated luminosity of 3.19~fb$^{-1}$. The result confirms the previous measurement by the CLEO Collaboration and is of greatly improved precision, which may deepen our understanding of the dynamical enhancement of the W-annihilation topology in the charmed meson decays

Observation and study of the decay J/ψ→ϕηη′J/\psi\rightarrow\phi\eta\eta'

We report the observation and study of the decay $J/\psi\rightarrow\phi\eta\eta'$ using $1.3\times{10^9}$ $J/\psi$ events collected with the BESIII detector. Its branching fraction, including all possible intermediate states, is measured to be $(2.32\pm0.06\pm0.16)\times{10^{-4}}$. We also report evidence for a structure, denoted as $X$, in the $\phi\eta'$ mass spectrum in the $2.0-2.1$ GeV/$c^2$ region. Using two decay modes of the $\eta'$ meson ($\gamma\pi^+\pi^-$ and $\eta\pi^+\pi^-$), a simultaneous fit to the $\phi\eta'$ mass spectra is performed. Assuming the quantum numbers of the $X$ to be $J^P = 1^-$, its significance is found to be 4.4$\sigma$, with a mass and width of $(2002.1 \pm 27.5 \pm 21.4)$ MeV/$c^2$ and $(129 \pm 17 \pm 9)$ MeV, respectively, and a product branching fraction $\mathcal{B}(J/\psi\rightarrow\eta{}X)\times{}\mathcal{B}(X\rightarrow\phi\eta')=(9.8 \pm 1.2 \pm 1.7)\times10^{-5}$. Alternatively, assuming $J^P = 1^+$, the significance is 3.8$\sigma$, with a mass and width of $(2062.8 \pm 13.1 \pm 7.2)$ MeV/$c^2$ and $(177 \pm 36 \pm 35)$ MeV, respectively, and a product branching fraction $\mathcal{B}(J/\psi\rightarrow\eta{}X)\times{}\mathcal{B}(X\rightarrow\phi\eta')=(9.6 \pm 1.4 \pm 2.0)\times10^{-5}$. The angular distribution of $J/\psi\rightarrow\eta{}X$ is studied and the two $J^P$ assumptions of the $X$ cannot be clearly distinguished due to the limited statistics. In all measurements the first uncertainties are statistical and the second systematic.Comment: 10 pages, 6 figures and 4 table

Observation of an anomalous line shape of the η′π+π−\eta^{\prime}\pi^{+}\pi^{-} mass spectrum near the ppˉp\bar{p} mass threshold in J/ψ→γη′π+π−J/\psi\rightarrow\gamma\eta^{\prime}\pi^{+}\pi^{-}

Using $1.09\times10^{9}$ $J/\psi$ events collected by the BESIII experiment in 2012, we study the $J/\psi\rightarrow\gamma\eta^{\prime}\pi^{+}\pi^{-}$ process and observe a significant abrupt change in the slope of the $\eta^{\prime}\pi^{+}\pi^{-}$ invariant mass distribution at the proton-antiproton ($p\bar{p}$) mass threshold. We use two models to characterize the $\eta^{\prime}\pi^{+}\pi^{-}$ line shape around $1.85~\text{GeV}/c^{2}$: one which explicitly incorporates the opening of a decay threshold in the mass spectrum (Flatt\'{e} formula), and another which is the coherent sum of two resonant amplitudes. Both fits show almost equally good agreement with data, and suggest the existence of either a broad state around $1.85~\text{GeV}/c^{2}$ with strong couplings to $p\bar{p}$ final states or a narrow state just below the $p\bar{p}$ mass threshold. Although we cannot distinguish between the fits, either one supports the existence of a $p\bar{p}$ molecule-like state or bound state with greater than $7\sigma$ significance

Observation of ηc→ωω\eta_c\to\omega\omega in J/ψ→γωωJ/\psi\to\gamma\omega\omega

Using a sample of $(1310.6\pm7.0)\times10^6$ $J/\psi$ events recorded with the BESIII detector at the symmetric electron positron collider BEPCII, we report the observation of the decay of the $(1^1 S_0)$ charmonium state $\eta_c$ into a pair of $\omega$ mesons in the process $J/\psi\to\gamma\omega\omega$. The branching fraction is measured for the first time to be $\mathcal{B}(\eta_c\to\omega\omega)= (2.88\pm0.10\pm0.46\pm0.68)\times10^{-3}$, where the first uncertainty is statistical, the second systematic and the third is from the uncertainty of $\mathcal{B}(J/\psi\to\gamma\eta_c)$. The mass and width of the $\eta_c$ are determined as $M=(2985.9\pm0.7\pm2.1)\,$MeV/$c^2$ and $\Gamma=(33.8\pm1.6\pm4.1)\,$MeV.Comment: 13 pages, 6 figure