On subgroups in division rings of type 22

Let $D$ be a division ring with center $F$. We say that $D$ is a {\em division ring of type $2$} if for every two elements $x, y\in D,$ the division subring $F(x, y)$ is a finite dimensional vector space over $F$. In this paper we investigate multiplicative subgroups in such a ring.Comment: 10 pages, 0 figure

Seesaw Right Handed Neutrino as the Sterile Neutrino for LSND

We show that a double seesaw framework for neutrino masses with $\mu-\tau$ exchange symmetry can lead to one of the righthanded seesaw partners of the light neutrinos being massless. This can play the role of a light sterile neutrino, giving a $3+1$ model that explains the LSND results. We get a very economical scheme, which makes it possible to predict the full $4\times 4$ neutrino mass matrix if CP is conserved. Once CP violation is included, effect of the LSND mass range sterile neutrino is to eliminate the lower bound on neutrinoless double beta decay rate which exists for the three neutrino case with inverted mass hierarchy. The same strategy can also be used to generate a natural $3+2$ model for LSND, which is also equally predictive for the CP conserving case in the limit of exact $\mu-\tau$ symmetry.Comment: 13 pages and one figure; model extended to 3+2 cas

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

A Comprehensive View of a Strongly Lensed Planck-Associated Submillimeter Galaxy

We present high-resolution maps of stars, dust, and molecular gas in a strongly lensed submillimeter galaxy (SMG) at z = 3.259. HATLAS J114637.9–001132 is selected from the Herschel-Astrophysical Terahertz Large Area Survey (H-ATLAS) as a strong lens candidate mainly based on its unusually high 500 μm flux density (~300 mJy). It is the only high-redshift Planck detection in the 130 deg^2 H-ATLAS Phase-I area. Keck Adaptive Optics images reveal a quadruply imaged galaxy in the K band while the Submillimeter Array and the Jansky Very Large Array show doubly imaged 880 μm and CO(1→0) sources, indicating differentiated distributions of the various components in the galaxy. In the source plane, the stars reside in three major kpc-scale clumps extended over ~1.6 kpc, the dust in a compact (~1 kpc) region ~3 kpc north of the stars, and the cold molecular gas in an extended (~7 kpc) disk ~5 kpc northeast of the stars. The emissions from the stars, dust, and gas are magnified by ~17, ~8, and ~7 times, respectively, by four lensing galaxies at z ~ 1. Intrinsically, the lensed galaxy is a warm (T_(dust) ~ 40-65 K), hyper-luminous (L_(IR) ~ 1.7 × 10^(13) L_☉; star formation rate (SFR) ~2000 M_☉ yr^(–1)), gas-rich (M_(gas)/M_(baryon) ~ 70%), young (M_(stellar)/SFR ~ 20 Myr), and short-lived (M_(gas)/SFR ~ 40 Myr) starburst. With physical properties similar to unlensed z > 2 SMGs, HATLAS J114637.9–001132 offers a detailed view of a typical SMG through a powerful cosmic microscope

Charmless Three-body Decays of B Mesons

Charmless 3-body decays of B mesons are studied in the framework of the factorization approach. The nonresonant contributions arising from $B\to P_1P_2$ transitions are evaluated using heavy meson chiral perturbation theory (HMChPT). The momentum dependence of nonresonant amplitudes is assumed to be in the exponential form e^{-\alpha_{NR}} p_B\cdot(p_i+p_j)} so that the HMChPT results are recovered in the soft meson limit $p_i, p_j\to 0$. In addition, we have identified another large source of the nonresonant signal in the matrix elements of scalar densities, e.g. $$, which can be constrained from the decay $\bar B^0\to K_SK_SK_S$ or $B^-\to K^-K_SK_S$. The intermediate vector meson contributions to 3-body decays are identified through the vector current, while the scalar meson resonances are mainly associated with the scalar density. Their effects are described in terms of the Breit-Wigner formalism. Our main results are: (i) All KKK modes are dominated by the nonresonant background. The predicted branching ratios of $K^+K^-K_{S(L)}$, $K^+K^-K^-$ and $K^-K_SK_S$ modes are consistent with the data within errors. (ii) Although the penguin-dominated $B^0\to K^+K^-K_{S}$ decay is subject to a potentially significant tree pollution, its effective $\sin 2\beta$ is very similar to that of the $K_SK_SK_S$ mode. However, direct CP asymmetry of the former, being of order -4%, is more prominent than the latter. (iii) For $B\to K\pi\pi$ decays, we found sizable nonresonant contributions in $K^-\pi^+\pi^-$ and $\bar K^0\pi^+\pi^-$ modes, in agreement with the Belle measurements but larger than the BaBar result.Comment: 39 pages, 2 figures, version to appear in PR

Natural Realizations of Seesaw in Mini-Warped Minimal SO(10)

The minimal SUSY SO(10) GUT models with {\bf 10}, {\bf 126} and {\bf 210} Higgs and only renormalizable couplings has been shown to provide a simple way to understand the neutrino mixings as well as the ratio $\Delta m^2_\odot/\Delta m^2_A$ in terms of quark mixing parameter $\theta_{Cabibbo}$, provided neutrino masses are described by type II seesaw formula. However, in this minimal picture, it is impossible to realize type II dominance with renormalizable couplings in 4-dimensions. We show that this problem can be cured by embedding this model into a warped 5-dimensional space time with warping between the Planck and the GUT scale, where both type II as well as mixed seesaw formulae can be realized in a natural manner without expanding the Higgs sector. These models also avoid the possible problem of threshold effects associated with large Higgs representations since the theory above the GUT scale is now strongly coupled.Comment: 20 pages and one figur

Supersymmetry Breaking by Type II Seesaw Assisted Anomaly Mediation

Anomaly mediated supersymmetry breaking (AMSB), when implemented in MSSM is known to suffer from the problem of negative slepton mass squared leading to breakdown of electric charge conservation. We show however that when MSSM is extended to explain small neutrino masses by including a pair of superheavy Higgs triplet superfields (the type II seesaw mechanism), the slepton masses can be deflected from the pure AMSB trajectory and become positive. In a simple model we present in this paper, the seesaw scale is about $10^{13}-10^{14}{\rm GeV}$. Gauge coupling unification can be maintained by embedding the triplet to SU(5) {\bf 15}-multiplet. In this scenario, bino is the LSP and its mass is nearly degenerate with NLSP slepton when the triplet mass is right around the seesaw scale.Comment: 18 pages, 4 figures, added references, added footnote

Phase-Dependent Spontaneous Spin Polarization and Bifurcation Delay in Coupled Two-Component Bose-Einstein Condensates

The spontaneous spin polarization and bifurcation delay in two-component Bose-Einstein condensates coupled with laser or/and radio-frequency pulses are investigated. We find that the bifurcation and the spontaneous spin polarization are determined by both physical parameters and relative phase between two condensates. Through bifurcations, the system enters into the spontaneous spin polarization regime from the Rabi regime. We also find that bifurcation delay appears when the parameter is swept through a static bifurcation point. This bifurcation delay is responsible for metastability leading to hysteresis.Comment: Improved version for cond-mat/021157

Conjecture on the Avoidance of the Big Crunch

KKLT give a mechanism to generate de Sitter vacua in string theory. And recently, the scenario, {\em landscape}, is suggested to explain the problem of the cosmological constant. In this scenario, the cosmological constant is a de Sitter vacuum. The vacuum is metastable and would decay into an anti-de Sitter vacuum finally. Then the catastrophe of the big crunch appears. In this paper by conjecturing the physics at the Planck scale, we modify the definition of the Hawking temperature. Hinted by this modification, we modify the Friedmann equation. we find that this avoid the singularity and gives a bouncing cosmological model.Comment: 6 page

Properties of weighted complex networks

We study two kinds of weighted networks, weighted small-world (WSW) and weighted scale-free (WSF). The weight $w_{ij}$ of a link between nodes $i$ and $j$ in the network is defined as the product of endpoint node degrees; that is $w_{ij}=(k_{i}k_{j})^{\theta}$. In contrast to adding weights to links during networks being constructed, we only consider weights depending on the `` popularity\rq\rq of the nodes represented by their connectivity. It was found that the both weighted networks have broad distributions on characterization the link weight, vertex strength, and average shortest path length. Furthermore, as a survey of the model, the epidemic spreading process in both weighted networks was studied based on the standard \emph{susceptible-infected} (SI) model. The spreading velocity reaches a peak very quickly after the infection outbreaks and an exponential decay was found in the long time propagation.Comment: 14 pages, 5 figure