Darboux and binary Darboux transformations for discrete integrable systems 1. Discrete potential KdV equation

The Hirota-Miwa equation can be written in `nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation. For both systems, we consider the Darboux and binary Darboux transformations, expressed in terms of the continuous variable, and obtain exact solutions in Wronskian and Grammian form. We discuss reductions of both systems to the discrete KdV and discrete potential KdV equations, respectively, and exploit this connection to find the Darboux and binary Darboux transformations and exact solutions of these equations

B\to X_s\gamma, X_s l^+ l^- decays and constraints on the mass insertion parameters in the MSSM

In this paper, we study the upper bounds on the mass insertion parameters $(\delta^{q}_{AB})_{ij}$ in the minimal supersymmetric standard model (MSSM). We found that the information from the measured branching ratio of $B \to X_s l^+ l^-$ decay can help us to improve the upper bounds on the mass insertions parameters \left (\delta^{u,d}_{AB})_{3j,i3}. Some regions allowed by the data of $Br(B \to X_s \gamma)$ are excluded by the requirement of a SM-like $C_{7\gamma}(m_b)$ imposed by the data of $Br(B \to X_s l^+ l^-)$.Comment: 16 pages, 5 eps figure files, typos remove

Do Linear Dispersions of Classical Waves Mean Dirac Cones?

By using the \vec{k}\cdot\vec{p} method, we propose a first-principles theory to study the linear dispersions in phononic and photonic crystals. The theory reveals that only those linear dispersions created by doubly-degenerate states can be described by a reduced Hamiltonian that can be mapped into the Dirac Hamiltonian and possess a Berry phase of -\pi. Triply-degenerate states can also generate Dirac-like cone dispersions, but the wavefunctions transform like a spin-1 particle and the Berry phase is zero. Our theory is capable of predicting accurately the linear slopes of Dirac/Dirac-like cones at various symmetry points in a Brilliouin zone, independent of frequency and lattice structure

Three-photon absorption in water-soluble ZnS nanocrystals

We report on large three-photon absorption (3PA) in glutathione-capped ZnS semiconductor nanocrystals (NCs), determined by both Z-scan and transient transmission techniques with 120-fs laser pulses. The monodispersed, water-soluble ZnS NCs are synthesized by a modified protocol with a mean diameter of 2.5 nm. Their 3PA cross-section is determined to be around 2.7x10^-78 cm^6s^2photon^-2 at an optimal wavelength of commercial Ti:sapphire femtosecond lasers. This value is nearly one order of magnitude greater than that of CdS NCs, and four to five orders of magnitude higher than those of the previously reported common UV fluorescent dyes.Comment: 15 pages, 4 figure

A Lumped Model for Rotational Modes in Phononic Crystals

We present a lumped model for the rotational modes induced by the rotational motion of individual scatterers in two-dimensional phononic crystals comprised of square arrays of solid cylindrical scatterers in solid hosts. The model provides a physical interpretation of the origin of the rotational modes, reveals the important role played by the rotational motion in the band structure, and reproduces the dispersion relations. The model increases the possibilities of wave manipulation in phononic crystals. In particular, expressions, derived from the model, for eigen-frequencies at high symmetry points unambiguously predict the presence of a new type of Dirac-like cone at the Brillouin center, which is found to be the result of accidental degeneracy of the rotational and dipolar modes

Categorization of species as native or nonnative using DNA sequence signatures without a complete reference library.

New genetic diagnostic approaches have greatly aided efforts to document global biodiversity and improve biosecurity. This is especially true for organismal groups in which species diversity has been underestimated historically due to difficulties associated with sampling, the lack of clear morphological characteristics, and/or limited availability of taxonomic expertise. Among these methods, DNA sequence barcoding (also known as "DNA barcoding") and by extension, meta-barcoding for biological communities, has emerged as one of the most frequently utilized methods for DNA-based species identifications. Unfortunately, the use of DNA barcoding is limited by the availability of complete reference libraries (i.e., a collection of DNA sequences from morphologically identified species), and by the fact that the vast majority of species do not have sequences present in reference databases. Such conditions are critical especially in tropical locations that are simultaneously biodiversity rich and suffer from a lack of exploration and DNA characterization by trained taxonomic specialists. To facilitate efforts to document biodiversity in regions lacking complete reference libraries, we developed a novel statistical approach that categorizes unidentified species as being either likely native or likely nonnative based solely on measures of nucleotide diversity. We demonstrate the utility of this approach by categorizing a large sample of specimens of terrestrial insects and spiders (collected as part of the Moorea BioCode project) using a generalized linear mixed model (GLMM). Using a training data set of known endemic (n = 45) and known introduced species (n = 102), we then estimated the likely native/nonnative status for 4,663 specimens representing an estimated 1,288 species (412 identified species), including both those specimens that were either unidentified or whose endemic/introduced status was uncertain. Using this approach, we were able to increase the number of categorized specimens by a factor of 4.4 (from 794 to 3,497), and the number of categorized species by a factor of 4.8 from (147 to 707) at a rate much greater than chance (77.6% accuracy). The study identifies phylogenetic signatures of both native and nonnative species and suggests several practical applications for this approach including monitoring biodiversity and facilitating biosecurity

Superconductivity suppression of Ba0.5K0.5Fe2-2xM2xAs2 single crystals by substitution of transition-metal (M = Mn, Ru, Co, Ni, Cu, and Zn)

We investigated the doping effects of magnetic and nonmagnetic impurities on the single-crystalline p-type Ba0.5K0.5Fe2-2xM2xAs2 (M = Mn, Ru, Co, Ni, Cu and Zn) superconductors. The superconductivity indicates robustly against impurity of Ru, while weakly against the impurities of Mn, Co, Ni, Cu, and Zn. However, the present Tc suppression rate of both magnetic and nonmagnetic impurities remains much lower than what was expected for the s\pm-wave model. The temperature dependence of resistivity data is observed an obvious low-T upturn for the crystals doped with high-level impurity, which is due to the occurrence of localization. Thus, the relatively weak Tc suppression effect from Mn, Co, Ni, Cu, and Zn are considered as a result of localization rather than pair-breaking effect in s\pm-wave model.Comment: 8 pages, 9 figures, to be published in Phys. Rev.

Observation of Many-body Dynamical Delocalization in a Kicked Ultracold Gas

Contrary to a driven classical system that exhibits chaos phenomena and diffusive energy growth, a driven quantum system can exhibit dynamical localization that features energy saturation. However, the evolution of the dynamically localized state in the presence of many-body interactions has long remained an open question. Here we experimentally study an interacting 1D ultracold gas periodically kicked by a pulsed optical lattice, and observe the interaction-driven emergence of dynamical delocalization and many-body quantum chaos. The observed dynamics feature a sub-diffusive energy growth manifest over a broad parameter range of interaction and kick strengths, and shed light on an area where theoretical approaches are extremely challenging.Comment: 14 pages, 11 figures including supplementary material

QED Renormalization Given in A Mass-Dependent Subtraction and The Renormalization Group Approach

The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge symmetry, the Lorentz- invariance and the mathematical convergence. Therefore, the renormalized results derived in the subtraction scheme are faithful and have no ambiguity. Especially, it is proved that the solution of the renormalization group equation satisfied by a renormalized wave function, propagator or vertex can be fixed by applying the renormalization boundary condition and, thus, an exact S-matrix element can be expressed in the form as written in the tree diagram approximation provided that the coupling constant and the fermion mass are replaced by their effective ones. In the one-loop approximation, the effective coupling constant and the effective fermion mass obtained by solving their renormalization group equations are given in rigorous and explicit expressions which are suitable in the whole range of distance and exhibit physically reasonable asymptotic behaviors.Comment: 29 pages, 4 figure