Experimental Realization of Br\"{u}schweiler's exponentially fast search algorithm in a homo-nuclear system

Compared with classical search algorithms, Grover quantum algorithm [ Phys. Rev. Lett., 79, 325(1997)] achieves quadratic speedup and Bruschweiler hybrid quantum algorithm [Phys. Rev. Lett., 85, 4815(2000)] achieves an exponential speedup. In this paper, we report the experimental realization of the Bruschweiler$ algorithm in a 3-qubit NMR ensemble system. The pulse sequences are used for the algorithms and the measurement method used here is improved on that used by Bruschweiler, namely, instead of quantitatively measuring the spin projection of the ancilla bit, we utilize the shape of the ancilla bit spectrum. By simply judging the downwardness or upwardness of the corresponding peaks in an ancilla bit spectrum, the bit value of the marked state can be read out, especially, the geometric nature of this read-out can make the results more robust against errors.Comment: 10 pages and 3 figure

On determination of the geometric cosmological constant from the OPERA experiment of superluminal neutrinos

The recent OPERA experiment of superluminal neutrinos has deep consequences in cosmology. In cosmology a fundamental constant is the cosmological constant. From observations one can estimate the effective cosmological constant $\Lambda_{eff}$ which is the sum of the quantum zero point energy $\Lambda_{dark energy}$ and the geometric cosmological constant $\Lambda$. The OPERA experiment can be applied to determine the geometric cosmological constant $\Lambda$. It is the first time to distinguish the contributions of $\Lambda$ and $\Lambda_{dark energy}$ from each other by experiment. The determination is based on an explanation of the OPERA experiment in the framework of Special Relativity with de Sitter space-time symmetry.Comment: 7 pages, no figure

Comparative tests on the performance of solar stills enhanced by pebbles, corrugated plate and membrane distillation and construction of performance prediction model for rock type still

To improve the water production capacity of solar still (SS), realize the theoretical prediction of the enhanced SS performance, and enrich the theoretical research basis of the desalination technology of SS, this paper sets up three kinds of enhancement measures, namely, rock, corrugated plate and membrane distillation, tests the enhanced water production effect, and reveals the enhanced operation mechanism. At the same time, a per- formance prediction model of rock enhanced was established based on the body-centered cubic stacking rock technology, and the influence of rock parameters on the distillation effect was studied. The study found that the water production increment of the three enhancement measures was concentrated in the rising period of the water production of the SS, and the total water production was 6.38 %, 12.30 % and 11.63 % higher than that of the traditional basin SS, respectively. The rock or corrugated plate enhances the distillation effect by elevating the seawater temperature and its temperature difference with the cover plate, and the membrane distillation increases the total water production through the additional water production of the membrane. Moreover, the constructed model can effectively predict the characteristics of rock enhanced SS. The increase in the rock layer thickness and the decrease in the rock particle size and material heat capacity both enhance the total daily water production, but the effect of rock particle size and material is weak. Although the increase of thickness increases the water production obviously, it aggravates the fluctuation of water production

Standard model plethystics

We study the vacuum geometry prescribed by the gauge invariant operators of the minimal supersymmetric standard model via the plethystic program. This is achieved by using several tricks to perform the highly computationally challenging Molien-Weyl integral, from which we extract the Hilbert series, encoding the invariants of the geometry at all degrees. The fully refined Hilbert series is presented as the explicit sum of 1422 rational functions. We found a good choice of weights to unrefine the Hilbert series into a rational function of a single variable, from which we can read off the dimension and the degree of the vacuum moduli space of the minimal supersymmetric standard model gauge invariants. All data in Mathematica format are also presented

Variation of the Fine-Structure Constant from the de Sitter Invariant Special Relativity

There are obvious discrepancies among various experimental constraints on the variation of the fine-structure constant, $\alpha$. We attempt to discuss the issue in the framework of de Sitter invariant Special Relativity (${\cal SR}_{c,R}$) and to present a possible solution to the disagreement. In addition, on the basis of the observational data and the discussions presented in this Letter, we derive a rough theoretical estimate of the radius of the Universe.Comment: 8 pages, no figure

Empirical modeling of the stellar spectrum of galaxies

An empirical method of modeling the stellar spectrum of galaxies is proposed, based on two successive applications of Principal Component Analysis (PCA). PCA is first applied to the newly available stellar library STELIB, supplemented by the J, H and K$_{s}$ magnitudes taken mainly from the 2 Micron All Sky Survey (2MASS). Next the resultant eigen-spectra are used to fit the observed spectra of a sample of 1016 galaxies selected from the Sloan Digital Sky Survey Data Release One (SDSS DR1). PCA is again applied, to the fitted spectra to construct the eigen-spectra of galaxies with zero velocity dispersion. The first 9 galactic eigen-spectra so obtained are then used to model the stellar spectrum of the galaxies in SDSS DR1, and synchronously to estimate the stellar velocity dispersion, the spectral type, the near-infrared SED, and the average reddening. Extensive tests show that the spectra of different type galaxies can be modeled quite accurately using these eigen-spectra. The method can yield stellar velocity dispersion with accuracies better than 10%, for the spectra of typical S/N ratios in SDSS DR1.Comment: 34 pages with 18 figures, submitted to A

Constraints on Lorentz invariance violation from gamma-ray burst GRB090510

We obtain modified dispersion relations by requiring the vanishing of determinant of inverse of modified photon propagators in Lorentz invariance violation (LIV) theory. Inspired by these dispersion relations, we give a more general dispersion relation with less assumption and apply it to the recent observed gamma-ray burst GRB090510 to extract various constraints on LIV parameters. We find that the constraint on quantum gravity mass is slightly larger than the Planck mass but is consistent with the other recent observations, so the corresponding LIV coefficient $\xi_1$ has reached the natural order ($o(1)$) as one expects. From our analysis, the linear LIV corrections to photon group velocity might be not excluded yet.Comment: 10 latex pages, no figures, version accepted for publication in PR