Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions

In connection with the weak null condition, Alinhac introduced a sufficient condition for global existence of small amplitude solutions to systems of semilinear wave equations in three space dimensions. We introduce a slightly weaker sufficient condition for the small data global existence, and we investigate the asymptotic pointwise behavior of global solutions for systems satisfying this condition. As an application, the asymptotic behavior of global solutions under the Alinhac condition is also derived.Comment: 56 pages, the final versio

Three-Dimensional Dirac Electrons at the Fermi Energy in Cubic Inverse Perovskites: Ca_3PbO and its Family

The band structure of cubic inverse perovskites, Ca_3PbO and its family, are investigated with the first-principles method. A close observation of the band structure reveals that six equivalent Dirac electrons with a very small mass exist on the line connecting the Gamma- and X-points, and at the symmetrically equivalent points in the Brillouin zone. The discovered Dirac electrons are three-dimensional and remarkably located exactly at the Fermi energy. A tight-binding model describing the low-energy band structure is also constructed and used to discuss the origin of the Dirac electrons in this material. Materials related to Ca_3PbO are also studied, and some design principles for the Dirac electrons in this series of materials are proposed.Comment: 4.2 pages, refined versio

Coherent Acoustic Perturbation of Second-Harmonic-Generation in NiO

We investigate the structural and magnetic origins of the unusual ultrafast second-harmonicgeneration (SHG) response of femtosecond-laser-excited nickel oxide (NiO) previously attributed to oscillatory reorientation dynamics of the magnetic structure induced by d-d excitations. Using time-resolved x-ray diffraction from the (3/2 3/2 3/2) magnetic planes, we show that changes in the magnitude of the magnetic structure factor following ultrafast optical excitation are limited to $\Delta/$ = 1.5% in the first 30 ps. An extended investigation of the ultrafast SHG response reveals a strong dependence on wavelength as well as characteristic echoes, both of which give evidence for an acoustic origin of the dynamics. We therefore propose an alternative mechanism for the SHG response based on perturbations of the nonlinear susceptibility via optically induced strain in a spatially confined medium. In this model, the two observed oscillation periods can be understood as the times required for an acoustic strain wave to traverse one coherence length of the SHG process in either the collinear or anti-collinear geometries.Comment: 26 pages, 7 figure

Seedling characteristics and retention of current photosynthates in leaves in relation to initial growth in pigeonpea (Cajanus cajan L. Millsp.) and cowpea (Vigna sinensis Endl.)

Improved varieties of pigeonpea (Cajanus cajan L. Millsp.) still retain some growth characteristics of perennial types of wild species such as slow seedling growth and rato on ability which are considered to be major yield-restricting characteristics when the growth period is shortened. Studies on the physiological background of slow initial growth may help improve the potential productivity of short-duration pigeonpea. It was found that the low seedling vigor of pigeonpea could be ascribed to the small seed size (Narayanan et al. 1981; Brakke and Gardner 1987), low rate of photosynthetic CO2 fixation (Rawson and Constable 1981), and low rates of metabolic processes (Huber and Hanson 1992; Ito et al. 1996). However, few authors have related the slow growth to the retention of current photosynthates and leaf respiration during the night. In contrast, seedling growth of cowpea (Vigna sinensis Endl.) was reported to be vigorous (Brakke and Gardner 1987). The objectives of this study were to characterize the initial growth of pigeonpea in comparison with cowpea. Two experiments were carried out, one dealing with growth analysis and the other with O2 uptake of leaf and retention of current photosynthates during the night

Raman Scattering Spectra of Elementary Electronic Excitations in Coupled Double-Quantum Well Structures

Using the time-dependent-local-density-approximation (TDLDA) within a self-consistent linear response theory, we calculate the elementary excitation energies and the associated inelastic light-scattering spectra of a strongly coupled two-component plasma in a double-quantum well system with electron occupation of symmetric and antisymmetric subbands. We find, consistent with the results of a recent experimental Raman scattering study, that the intersubband spin density excitations tend to merge with the single particle excitations (i.e. the excitonic shift decreases monotonically) as the Fermi energy increases beyond the symmetric-antisymmetric energy gap $\bigtriangleup_{SAS}$. However, our TDLDA calculation does not show the abrupt suppresion of the excitonic shift seen experimentally at a finite value of the subband occupancy parameter $\eta \equiv \bigtriangleup_{\text{SAS}} / E_{\text{F}}$.Comment: 9 pages, RevTeX, 5 figures available upon request, PIT-SDS-00

Low-Energy Effective Hamiltonian and the Surface States of Ca_3PbO

The band structure of Ca_3PbO, which possesses a three-dimensional massive Dirac electron at the Fermi energy, is investigated in detail. Analysis of the orbital weight distributions on the bands obtained in the first-principles calculation reveals that the bands crossing the Fermi energy originate from the three Pb-p orbitals and three Ca-dx2y2 orbitals. Taking these Pb-p and Ca-dx2y2 orbitals as basis wave functions, a tight-binding model is constructed. With the appropriate choice of the hopping integrals and the strength of the spin-orbit coupling, the constructed model sucessfully captures important features of the band structure around the Fermi energy obtained in the first-principles calculation. By applying the suitable basis transformation and expanding the matrix elements in the series of the momentum measured from a Dirac point, the low-energy effective Hamiltonian of this model is explicitely derived and proved to be a Dirac Hamiltonain. The origin of the mass term is also discussed. It is shown that the spin-orbit coupling and the orbitals other than Pb-p and Ca-dx2y2 orbitals play important roles in making the mass term finite. Finally, the surface band structures of Ca_3PbO for several types of surfaces are investigated using the constructed tight-binding model. We find that there appear nontrivial surface states that cannot be explained as the bulk bands projected on the surface Brillouin zone. The relation to the topological insulator is also discussed.Comment: 11 page

Superconductivity at 38 K in Iron-Based Compound with Platinum-Arsenide Layers Ca10(Pt4As8)(Fe2-xPtxAs2)5

We report superconductivity in novel iron-based compounds Ca10(PtnAs8)(Fe2-xPtxAs2)5 with n = 3 and 4. Both compounds crystallize in triclinic structures (space group P-1), in which Fe2As2 layers alternate with PtnAs8 spacer layers. Superconductivity with a transition temperature of 38 K is observed in the n = 4 compound with a Pt content of x ~ 0.36 in the Fe2As2 layers. The compound with n = 3 exhibits superconductivity at 13 K.Comment: OPEN SELECT article, 11 pages, 5 figures, 2 table

Multi-Channel Kondo Necklace

A multi--channel generalization of Doniach's Kondo necklace model is formulated, and its phase diagram studied in the mean--field approximation. Our intention is to introduce the possible simplest model which displays some of the features expected from the overscreened Kondo lattice. The $N$ conduction electron channels are represented by $N$ sets of pseudospins \vt_{j}, $j=1, ... , N$, which are all antiferromagnetically coupled to a periodic array of |\vs|=1/2 spins. Exploiting permutation symmetry in the channel index $j$ allows us to write down the self--consistency equation for general $N$. For $N>2$, we find that the critical temperature is rising with increasing Kondo interaction; we interpret this effect by pointing out that the Kondo coupling creates the composite pseudospin objects which undergo an ordering transition. The relevance of our findings to the underlying fermionic multi--channel problem is discussed.Comment: 29 pages (2 figures upon request from [email protected]), LATEX, submitted for publicatio

Trimer Formation and Metal-Insulator Transition in Orbital Degenerate Systems on a Triangular Lattice

As a prototypical self-organization in the system with orbital degeneracy, we theoretically investigate trimer formation on a triangular lattice, as observed in LiVO2. From the analysis of an effective spin-orbital coupled model in the strong correlation limit, we show that the previously-proposed orbital-ordered trimer state is not the lowest-energy state for a finite Hund's-rule coupling. Instead, exploring the ground state in a wide range of parameters for a multiorbital Hubbard model, we find an instability toward a different orbital-ordered trimer state in the intermediately correlated regime in the presence of trigonal crystal field. The trimer phase appears in the competing region among a paramagnetic metal, band insulator, and Mott insulator. The underlying mechanism is nesting instability of the Fermi surface by a synergetic effect of Coulomb interactions and trigonal-field splitting. The results are compared with experiments in triangularlattice compounds, LiVX2 (X=O, S, Se) and NaVO2.Comment: 4 pages, 4 figures, accepted for publication in J. Phys. Soc. Jp