Three-dimensional structures of the spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in PT-symmetric potentials

The spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in PT-symmetric potentials is investigated, and two families of analytical three-dimensional spatiotemporal structure solutions are obtained. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results indicate that solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the self-focusing medium, while they are always unstable for all parameters in the self-defocusing medium. Moreover, some dynamical properties of these solutions are discussed, such as the phase switch, power and transverse power-flow density. The span of phase switch gradually enlarges with the decrease of the competing parameter k in PT-symmetric potentials. The power and power-flow density are all positive, which implies that the power flow and exchange from the gain toward the loss domains in the PT cell.Funded by the National Natural Science Foundation of China (Grant No. 11375007), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY13F050006)

Optimal Nested Test Plan for Combinatorial Quantitative Group Testing

We consider the quantitative group testing problem where the objective is to identify defective items in a given population based on results of tests performed on subsets of the population. Under the quantitative group testing model, the result of each test reveals the number of defective items in the tested group. The minimum number of tests achievable by nested test plans was established by Aigner and Schughart in 1985 within a minimax framework. The optimal nested test plan offering this performance, however, was not obtained. In this work, we establish the optimal nested test plan in closed form. This optimal nested test plan is also order optimal among all test plans as the population size approaches infinity. Using heavy-hitter detection as a case study, we show via simulation examples orders of magnitude improvement of the group testing approach over two prevailing sampling-based approaches in detection accuracy and counter consumption. Other applications include anomaly detection and wideband spectrum sensing in cognitive radio systems

QCD corrections to e^+ e^- to J/\psi(\psi(2S))+\chi_{cJ} (J=0,1,2) at B Factories

We analytically calculate the cross sections of double charmonium production in $e^+ e^- \to J/\psi(\psi(2S))\chi_{cJ}$ (J=0,1,2) at next-to-leading order (NLO) in $\alpha_s$ in nonrelativistic QCD, and confirm factorization of these processes. In contrast to $\chi_{c0}$ production, for which the NLO correction is large and positive, the NLO corrections for $\chi_{c1,2}$ production can be negative, resulting in decreased $K$ factors of 0.91 and 0.78 for J=1 and 2 respectively when $\mu = 2 m_{c}$. Consequently, the NLO QCD corrections markedly enlarge the difference between cross sections of $\chi_{c0}$ and $\chi_{c1,2}$. This may explain why $e^+ e^- \to J/\psi(\psi(2S))\chi_{c0}$ but not $e^+ e^- \to J/\psi(\psi(2S))\chi_{c1,2}$ is observed experimentally. Moreover, for $J/\psi(\psi(2S))\chi_{c1,2}$, the NLO QCD corrections substantially reduce the $\mu$ dependence and lead to predictions with small theoretical uncertainties.Comment: Version published in PRD, 6 pages, 3 figures, 2 tables, one reference adde

J/psi (psi') production at the Tevatron and LHC at O(\alpha_s^4v^4) in nonrelativistic QCD

We present a complete evaluation for \jpsi(\psip) prompt production at the Tevatron and LHC at next-to-leading order in nonrelativistic QCD, including color-singlet, color-octet, and higher charmonia feeddown contributions. The short-distance coefficients of \pj at next-to-leading order are found to be larger than leading order by more than an order of magnitude but with a minus sign at high transverse momentum $p_T$. Two new linear combinations of color-octet matrix elements are obtained from the CDF data, and used to predict \jpsi production at the LHC, which agrees with the CMS data. The possibility of \sa dominance and the \jpsi polarization puzzle are also discussed.Comment: Version published in PRL, 4 pages, 4 figure

Connecting Neutrino Masses and Dark Matter by High-dimensional Lepton Number Violation Operator

We propose a new model with the Majorana neutrino masses generated at two-loop level, in which the lepton number violation (LNV) processes, such as neutrinoless double beta decays, are mainly induced by the dimension-7 LNV effective operator O_7=\bar l_R^c \gamma^\mu L_L(D_mu \Phi) \Phi \Phi. Note that it is necessary to impose an Z_2 symmetry in order that O_7 dominates over the conventional dimension-5 Weinberg operator, which naturally results in a stable Z_2-odd neutral particle to be the cold dark matter candidate. More interestingly, due to the non-trivial dependence of the charged lepton masses, the model predicts the neutrino mass matrix to be in the form of the normal hierarchy. We also focus on a specific parameter region of great phenomenological interests, such as electroweak precision tests, dark matter direct searches along with its relic abundance, and lepton flavor violation processes.Comment: 19 pages, 5 figure