Hadamard States and Two-dimensional Gravity

We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.Comment: 7 pages, no figur

Spin-Driven Nematic Instability of the Multi-Orbital Hubbard Model: Application to Iron-Based Superconductors

Nematic order resulting from the partial melting of density-waves has been proposed as the mechanism to explain nematicity in iron-based superconductors. An outstanding question, however, is whether the microscopic electronic model for these systems -- the multi-orbital Hubbard model -- displays such an ordered state as its leading instability. In contrast to usual electronic instabilities, such as magnetic and charge order, this fluctuation-driven phenomenon cannot be captured by the standard RPA method. Here, by including fluctuations beyond RPA in the multi-orbital Hubbard model, we derive its nematic susceptibility and contrast it with its ferro-orbital order susceptibility, showing that its leading instability is the spin-driven nematic phase. Our results also demonstrate the primary role played by the $d_{xy}$ orbital in driving the nematic transition, and reveal that high-energy magnetic fluctuations are essential to stabilize nematic order in the absence of magnetic order.Comment: 8 pages, 6 figure

Wave Profile for Current Bearing Antiforce Waves

For fluid dynamical analysis of breakdown waves, we employ a one-dimensional, three-component (electrons, ions and neutral particles) fluid model to describe a steady-state, ionizing wave propagating counter to strong electric fields. The electron gas temperature and therefore the electron fluid pressure is assumed to be large enough to sustain the wave motion down the discharge tube. Such waves are referred to as antiforce waves. The complete set of equations describing such waves consists of the equations of conservation of mass, momentum and energy coupled with Poisson’s equation. Inclusion of current behind the wave front alters the set of electron fluid dynamical equations and also the boundary condition on electron temperature. For a range of experimentally observed current values, using the modified boundary condition on electron temperature, we have been able to integrate our modified set of electron fluid dynamical equations through the Debye layer. Our solutions meet the expected boundary conditions at the trailing edge of the wave. We present the wave profile for electric field, electron velocity, electron number density and electron temperature within the Debye layer of the wave

Role of multiorbital effects in the magnetic phase diagram of iron-pnictides

We elucidate the pivotal role of the bandstructure's orbital content in deciding the type of commensurate magnetic order stabilized within the itinerant scenario of iron-pnictides. Recent experimental findings in the tetragonal magnetic phase attest to the existence of the so-called charge and spin ordered density wave over the spin-vortex crystal phase, the latter of which tends to be favored in simplified band models of itinerant magnetism. Here we show that employing a multiorbital itinerant Landau approach based on realistic bandstructures can account for the experimentally observed magnetic phase, and thus shed light on the importance of the orbital content in deciding the magnetic order. In addition, we remark that the presence of a hole pocket centered at the Brillouin zone's ${\rm M}$-point favors a magnetic stripe rather than a tetragonal magnetic phase. For inferring the symmetry properties of the different magnetic phases, we formulate our theory in terms of magnetic order parameters transforming according to irreducible representations of the ensuing D$_{\rm 4h}$ point group. The latter method not only provides transparent understanding of the symmetry breaking schemes but also reveals that the leading instabilities always belong to the $\{A_{1g},B_{1g}\}$ subset of irreducible representations, independent of their C$_2$ or C$_4$ nature.Comment: 11 pages, 6 figure

Lattice vibrations and structural instability in Cesium near the cubic to tetragonal transition

Under pressure cesium undergoes a transition from a high-pressure fcc phase (Cs-II) to a collapsed fcc phase (Cs-III) near 4.2GPa. At 4.4GPa there follows a transition to the tetragonal Cs-IV phase. In order to investigate the lattice vibrations in the fcc phase and seek a possible dynamical instability of the lattice, the phonon spectra of fcc-Cs at volumes near the III-IV transition are calculated using Savrasov's density functional linear-response LMTO method. Compared with quasiharmonic model calculations including non-central interatomic forces up to second neighbours, at the volume $V/V_0= 0.44$ ($V_0$ is the experimental volume of bcc-Cs with $a_0$=6.048{\AA}), the linear-response calculations show soft intermediate wavelength $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons. Similar softening is also observed for short wavelength $L[\xi\xi\xi]$ and $L[00\xi]$ phonons and intermediate wavelength $L[\xi\xi\xi]$ phonons. The Born-von K\'{a}rm\'{a}n analysis of dispersion curves indicates that the interplanar force constants exhibit oscillating behaviours against plane spacing $n$ and the large softening of intermediate wavelength $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons results from a negative (110)-interplanar force-constant $\Phi_{n=2}$. The frequencies of the $T_{[1\bar{1}0]}[{\xi}{\xi}0]$ phonons with $\xi$ around 1/3 become imaginary and the fcc structure becomes dynamically unstable for volumes below $0.41V_0$. It is suggested that superstructures corresponding to the $\mathbf{q}{\neq}0$ soft mode should be present as a precursor of tetragonal Cs-IV structure.Comment: 12 pages, 5 figure

Testing strong line metallicity diagnostics at z~2

High-z galaxy gas-phase metallicities are usually determined through observations of strong optical emission lines with calibrations tied to the local universe. Recent debate has questioned if these calibrations are valid in the high-z universe. We investigate this by analysing a sample of 16 galaxies at z~2 available in the literature, and for which the metallicity can be robustly determined using oxygen auroral lines. The sample spans a redshift range of 1.4 < z < 3.6, has metallicities of 7.4-8.4 in 12+log(O/H) and stellar masses 10^7.5-10^11 Msun. We test commonly used strong line diagnostics (R23, O3, O2, O32, N2, O3N2 and Ne3O2 ) as prescribed by four different sets of empirical calibrations, as well as one fully theoretical calibration. We find that none of the strong line diagnostics (or calibration set) tested perform consistently better than the others. Amongst the line ratios tested, R23 and O3 deliver the best results, with accuracies as good as 0.01-0.04 dex and dispersions of ~0.2 dex in two of the calibrations tested. Generally, line ratios involving nitrogen predict higher values of metallicity, while results with O32 and Ne3O2 show large dispersions. The theoretical calibration yields an accuracy of 0.06 dex, comparable to the best strong line methods. We conclude that, within the metallicity range tested in this work, the locally calibrated diagnostics can still be reliably applied at z~2.Comment: 12 pages, 8 Figures, accepted for publication in MNRA

Stochastics theory of log-periodic patterns

We introduce an analytical model based on birth-death clustering processes to help understanding the empirical log-periodic corrections to power-law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastics theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of cooperative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t_{o} is derived in terms of birth-death clustering coefficients.Comment: LaTeX, 1 ps figure - To appear J. Phys. A: Math & Ge