A Provably Stable Discontinuous Galerkin Spectral Element Approximation for Moving Hexahedral Meshes

We design a novel provably stable discontinuous Galerkin spectral element (DGSEM) approximation to solve systems of conservation laws on moving domains. To incorporate the motion of the domain, we use an arbitrary Lagrangian-Eulerian formulation to map the governing equations to a fixed reference domain. The approximation is made stable by a discretization of a skew-symmetric formulation of the problem. We prove that the discrete approximation is stable, conservative and, for constant coefficient problems, maintains the free-stream preservation property. We also provide details on how to add the new skew-symmetric ALE approximation to an existing discontinuous Galerkin spectral element code. Lastly, we provide numerical support of the theoretical results

Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals

We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern number, vanishes). Following the approach used recently to develop the single-band formalism [T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. {\bf 95}, 137205 (2005)], we work in the Wannier representation and find that the magnetization is comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior and an unexpected one arising from net currents carried by Wannier functions near the surface. Unlike the single-band case, where each of these contributions is separately gauge-invariant, in the multi-band formulation only the \emph{sum} of both terms is gauge-invariant. Our final expression for the orbital magnetization can be rewritten as a bulk property in terms of Bloch functions, making it simple to implement in modern code packages. The reciprocal-space expression is evaluated for 2d model systems and the results are verified by comparing to the magnetization computed for finite samples cut from the bulk. Finally, while our formal proof is limited to normal insulators, we also present a heuristic extension to Chern insulators (having nonzero Chern invariant) and to metals. The validity of this extension is again tested by comparing to the magnetization of finite samples cut from the bulk for 2d model systems. We find excellent agreement, thus providing strong empirical evidence in favor of the validity of the heuristic formula.Comment: 14 pages, 8 figures. Fixed a typo in appendix

Experimental Demonstration of Greenberger-Horne-Zeilinger Correlations Using Nuclear Magnetic Resonance

The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum correlations that cannot be explained by classical local hidden variables. This paper reports on the experimental realization of GHZ correlations using nuclear magnetic resonance (NMR). The NMR experiment differs from the originally proposed GHZ experiment in several ways: it is performed on mixed states rather than pure states; and instead of being widely separated, the spins on which it is performed are all located in the same molecule. As a result, the NMR version of the GHZ experiment cannot entirely rule out classical local hidden variables. It nonetheless provides an unambiguous demonstration of the "paradoxical" GHZ correlations, and shows that any classical hidden variables must communicate by non-standard and previously undetected forces. The NMR demonstration of GHZ correlations shows the power of NMR quantum information processing techniques for demonstrating fundamental effects in quantum mechanics.Comment: Latex2.09, 8 pages, 1 eps figur

Neutral Higgs-pair production at Linear Colliders within the general 2HDM: quantum effects and triple Higgs boson self-interactions

The pairwise production of neutral Higgs bosons is analyzed in the context of the future linear colliders, such as the ILC and CLIC, within the general Two-Higgs-Doublet Model (2HDM). The corresponding cross-sections are computed at the one-loop level in full compliance with the current phenomenological bounds and the stringent theoretical constraints inherent to the consistency of the model. We uncover regions across the 2HDM parameter space, mainly for low tan\beta near 1 and moderate values of the relevant lambda_5 parameter, wherein the radiative corrections to the Higgs-pair production cross sections can comfortably reach 50% This behavior can be traced back to the enhancement capabilities of the trilinear Higgs self-interactions -- a trademark feature of the 2HDM, with no counterpart in the Minimal Supersymmetric Standard Model. Interestingly enough, the quantum effects are positive for energies around 500 GeV, thereby producing a significant enhancement in the expected number of events precisely around the fiducial startup energy of the ILC. The Higgs-pair production rates can be substantial, typically amounting to a few thousand events per 500 inverse femtobarn of integrated luminosity. In contrast, the corrections are negative in the highest energy range (1 TeV). We also compare the exclusive pairwise production of Higgs bosons with the inclusive gauge boson fusion channels leading to 2H+X finals states, and also with the exclusive triple Higgs boson production. We find that these multiparticle final states can be highly complementary in the overall Higgs bosons search strategy.Comment: 42 pages, 23 figures, 10 tables. Accepted in Phys. Rev. D (the published version is shorter

X-ray Emission from Young Stellar Objects in the \epsilon Chamaeleontis Group: the Herbig Ae Star HD 104237 and Associated Low-Mass Stars

We present Chandra-HETGS observations of the Herbig Ae star HD 104237 and the associated young stars comprising lower mass stars, in the 0.15-1.75\msol mass range, in their pre-main sequence phase. The brightest X-ray source in the association is the central system harboring the Herbig Ae primary, and a K3 companion. Its X-ray variability indicates modulation possibly on time scales of the rotation period of the Herbig Ae star, and this would imply that the primary significantly contributes to the overall emission. The spectrum of the Herbig Ae+K3 system shows a soft component significantly more pronounced than in other K-type young stars. This soft emission is reminiscent of the unusually soft spectra observed for the single Herbig Ae stars HD 163296 and AB Aur, and therefore we tentatively attribute it to the Herbig Ae of the binary system. The HETGS spectrum shows strong emission lines corresponding to a wide range of plasma temperatures. The He-like triplet of MgXI and NeIX suggest the presence of plasma at densities of about $10^{12}$ cm$^{-3}$, possibly indicating accretion related X-ray production mechanism. The analysis of the zero-order spectra of the other sources indicates X-ray emission characteristics typical of pre-main sequence stars of similar spectral type, with the exception of the T Tauri HD104237-D, whose extremely soft emission is very similar to the emission of the classical T Tauri star TW Hya, and suggests X-ray production by shocked accreting plasma.Comment: accepted for publication on the Astrophysical Journa

Two-Dimensional Hydrodynamics of Pre-Core Collapse: Oxygen Shell Burning

By direct hydrodynamic simulation, using the Piecewise Parabolic Method (PPM) code PROMETHEUS, we study the properties of a convective oxygen burning shell in a SN 1987A progenitor star prior to collapse. The convection is too heterogeneous and dynamic to be well approximated by one-dimensional diffusion-like algorithms which have previously been used for this epoch. Qualitatively new phenomena are seen. The simulations are two-dimensional, with good resolution in radius and angle, and use a large (90-degree) slice centered at the equator. The microphysics and the initial model were carefully treated. Many of the qualitative features of previous multi-dimensional simulations of convection are seen, including large kinetic and acoustic energy fluxes, which are not accounted for by mixing length theory. Small but significant amounts of carbon-12 are mixed non-uniformly into the oxygen burning convection zone, resulting in hot spots of nuclear energy production which are more than an order of magnitude more energetic than the oxygen flame itself. Density perturbations (up to 8%) occur at the `edges' of the convective zone and are the result of gravity waves generated by interaction of penetrating flows into the stable region. Perturbations of temperature and electron fraction at the base of the convective zone are of sufficient magnitude to create angular inhomogeneities in explosive nucleosynthesis products, and need to be included in quantitative estimates of yields. Combined with the plume-like velocity structure arising from convection, the perturbations will contribute to the mixing of nickel-56 throughout supernovae envelopes. Runs of different resolution, and angular extent, were performed to test the robustness of theseComment: For mpeg movies of these simulations, see http://www.astrophysics.arizona.edu/movies.html Submitted to the Astrophysical Journa

The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative hamiltonian method, a concrete example where Lorentz invariance of individual events is broken.Comment: Final version. See also http://www.cosmologia.cbpf.b

A back-to-front derivation: the equal spacing of quantum levels is a proof of simple harmonic oscillator physics

The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one mapping between the provision of equally spaced quantum energy levels and simple harmonic motion. The analysis establishes that the Hamiltonian of any system featuring quantized energy levels in an evenly spaced, infinite set must have a quadratic dependence on a pair of canonically conjugate variables. Moreover, specific physical inferences can be drawn. For example, exploiting this 'back-to-front' derivation, and based on the known existence of photons, it can be proved that an electromagnetic energy density is quadratic in both the electric and magnetic fields