The trouble with asymptotically safe inflation

In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.Comment: 13 pages, 1 figur

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)

Bottomonium Spectrum with Screened Potential

As a sister work of Ref.[1], we incorporate the color-screening effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate the effects of screened potential on the spectrum of bottomonium. We calculate the masses, electromagnetic decays, and E1 transitions of bottomonium states. We find that the fine splittings between $\chi_{bJ}$ (J=0,1,2) states are in good agreement with experimental data, and the E1 transition rates of $\Upsilon(2S)\to\gamma\chi_{bJ}(1P)$ and $\Upsilon(3S)\to\gamma\chi_{bJ}(2P)$ (J=0,1,2) all agree with data within experimental errors. In particular, the mass of $\Upsilon(6S)$ is lowered down to match that of the $\Upsilon(11020)$, which is smaller than the predictions of the linear potential models by more than 100 MeV. Comparison between charmonium and bottomonium in some related problems is also discussed.Comment: 9 pages, Commun. Theor. Phys. (in press

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