Semiclassical approximation with zero velocity trajectories

We present a new semiclassical method that yields an approximation to the quantum mechanical wavefunction at a fixed, predetermined position. In the approach, a hierarchy of ODEs are solved along a trajectory with zero velocity. The new approximation is local, both literally and from a quantum mechanical point of view, in the sense that neighboring trajectories do not communicate with each other. The approach is readily extended to imaginary time propagation and is particularly useful for the calculation of quantities where only local information is required. We present two applications: the calculation of tunneling probabilities and the calculation of low energy eigenvalues. In both applications we obtain excellent agrement with the exact quantum mechanics, with a single trajectory propagation.Comment: 16 pages, 7 figure

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

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

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

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

Optimization of inhomogeneous electron correlation factors in periodic solids

A method is presented for the optimization of one-body and inhomogeneous two-body terms in correlated electronic wave functions of Jastrow-Slater type. The most general form of inhomogeneous correlation term which is compatible with crystal symmetry is used and the energy is minimized with respect to all parameters using a rapidly convergent iterative approach, based on Monte Carlo sampling of the energy and fitting energy fluctuations. The energy minimization is performed exactly within statistical sampling error for the energy derivatives and the resulting one- and two-body terms of the wave function are found to be well-determined. The largest calculations performed require the optimization of over 3000 parameters. The inhomogeneous two-electron correlation terms are calculated for diamond and rhombohedral graphite. The optimal terms in diamond are found to be approximately homogeneous and isotropic over all ranges of electron separation, but exhibit some inhomogeneity at short- and intermediate-range, whereas those in graphite are found to be homogeneous at short-range, but inhomogeneous and anisotropic at intermediate- and long-range electron separation.Comment: 23 pages, 15 figures, 1 table, REVTeX4, submitted to PR

Coming down from the trees: is terrestrial activity in Bornean orangutans natural or disturbance driven?

The orangutan is the world's largest arboreal mammal, and images of the red ape moving through the tropical forest canopy symbolise its typical arboreal behaviour. Records of terrestrial behaviour are scarce and often associated with habitat disturbance. We conducted a large-scale species-level analysis of ground-based camera-trapping data to evaluate the extent to which Bornean orangutans Pongo pygmaeus come down from the trees to travel terrestrially, and whether they are indeed forced to the ground primarily by anthropogenic forest disturbances. Although the degree of forest disturbance and canopy gap size influenced terrestriality, orangutans were recorded on the ground as frequently in heavily degraded habitats as in primary forests. Furthermore, all age-sex classes were recorded on the ground (flanged males more often). This suggests that terrestrial locomotion is part of the Bornean orangutan's natural behavioural repertoire to a much greater extent than previously thought, and is only modified by habitat disturbance. The capacity of orangutans to come down from the trees may increase their ability to cope with at least smaller-scale forest fragmentation, and to cross moderately open spaces in mosaic landscapes, although the extent of this versatility remains to be investigated

Hyperentangled States

We investigate a new class of entangled states, which we call 'hyperentangled',that have EPR correlations identical to those in the vacuum state of a relativistic quantum field. We show that whenever hyperentangled states exist in any quantum theory, they are dense in its state space. We also give prescriptions for constructing hyperentangled states that involve an arbitrarily large collection of systems.Comment: 23 pages, LaTeX, Submitted to Physical Review