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

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

Investigation of the spin-glass regime between the antiferromagnetic and superconducting phases in Fe1+y_{1+y}Sex_xTe1−x_{1-x}

Using bulk magnetization along with elastic and inelastic neutron scattering techniques, we have investigated the phase diagram of Fe$_{1+y}$Se$_{x}$Te$_{1-x}$ and the nature of magnetic correlations in three nonsuperconducting samples of Fe$_{1.01}$Se$_{0.1}$Te$_{0.9}$, Fe$_{1.01}$Se$_{0.15}$Te$_{0.85}$ and Fe$_{1.02}$Se$_{0.3}$Te$_{0.7}$. A cusp and hysteresis in the temperature dependence of the magnetization for the $x=0.15$ and 0.3 samples indicates spin-glass (SG) ordering below $T_{\rm sg} = 23$K. Neutron scattering measurements indicate that the spin-glass behavior is associated with short-range spin density wave (SDW) ordering characterized by a static component and a low-energy dynamic component with a characteristic incommensurate wave vector of ${\bf Q}_m = (0.46, 0, 0.50)$ and an anisotropy gap of $\sim$ 2.5 meV. Our high ${\bf Q}$-resolution data also show that the systems undergo a glassy structural distortion that coincides with the short-range SDW order

Global existence for coupled systems of nonlinear wave and Klein-Gordon equations in three space dimensions

We consider the Cauchy problem for coupled systems of wave and Klein-Gordon equations with quadratic nonlinearity in three space dimensions. We show global existence of small amplitude solutions under certain condition including the null condition on self-interactions between wave equations. Our condition is much weaker than the strong null condition introduced by Georgiev for this kind of coupled system. Consequently our result is applicable to certain physical systems, such as the Dirac-Klein-Gordon equations, the Dirac-Proca equations, and the Klein-Gordon-Zakharov equations.Comment: 31 pages. The final versio

Coupling of spin and orbital excitations in the iron-based superconductor FeSe(0.5)Te(0.5)

We present a combined analysis of neutron scattering and photoemission measurements on superconducting FeSe(0.5)Te(0.5). The low-energy magnetic excitations disperse only in the direction transverse to the characteristic wave vector (1/2,0,0), whereas the electronic Fermi surface near (1/2,0,0) appears to consist of four incommensurate pockets. While the spin resonance occurs at an incommensurate wave vector compatible with nesting, neither spin-wave nor Fermi-surface-nesting models can describe the magnetic dispersion. We propose that a coupling of spin and orbital correlations is key to explaining this behavior. If correct, it follows that these nematic fluctuations are involved in the resonance and could be relevant to the pairing mechanism.Comment: 4 pages, 4 figures; accepted versio

Correlation induced phonon softening in low density coupled bilayer systems

We predict a possible phonon softening instability in strongly correlated coupled semiconductor bilayer systems. By studying the plasmon-phonon coupling in coupled bilayer structures, we find that the renormalized acoustic phonon frequency may be softened at a finite wave vector due to many-body local field corrections, particularly in low density systems where correlation effects are strong. We discuss experimental possibilities to search for this predicted phonon softening phenomenon.Comment: 4 pages with 2 figure