Ground-based adaptive optics coronagraphic performance under closed-loop predictive control

The discovery of the exoplanet Proxima b highlights the potential for the coming generation of giant segmented mirror telescopes (GSMTs) to characterize terrestrial --- potentially habitable --- planets orbiting nearby stars with direct imaging. This will require continued development and implementation of optimized adaptive optics systems feeding coronagraphs on the GSMTs. Such development should proceed with an understanding of the fundamental limits imposed by atmospheric turbulence. Here we seek to address this question with a semi-analytic framework for calculating the post-coronagraph contrast in a closed-loop AO system. We do this starting with the temporal power spectra of the Fourier basis calculated assuming frozen flow turbulence, and then apply closed-loop transfer functions. We include the benefits of a simple predictive controller, which we show could provide over a factor of 1400 gain in raw PSF contrast at 1 $\lambda/D$ on bright stars, and more than a factor of 30 gain on an I = 7.5 mag star such as Proxima. More sophisticated predictive control can be expected to improve this even further. Assuming a photon noise limited observing technique such as High Dispersion Coronagraphy, these gains in raw contrast will decrease integration times by the same large factors. Predictive control of atmospheric turbulence should therefore be seen as one of the key technologies which will enable ground-based telescopes to characterize terrrestrial planets.Comment: Accepted to JATI

Maximally-localized Wannier functions for entangled energy bands

We present a method for obtaining well-localized Wannier-like functions (WFs) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally-localized WFs method (N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12847 (1997)) that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally-localized WFs for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WFs which are centered at the tetrahedral interstitial sites, suggesting an alternative tight-binding parametrization.Comment: 13 pages, with 9 postscript figures embedded. Uses REVTEX and epsf macro

Conductance fingerprints of non-collinear magnetic states in single atom contacts: a first-principles Wannier functions study

We present a first-principles computational scheme for investigating the ballistic transport properties of one-dimensional nanostructures with non-collinear magnetic order. The electronic structure is obtained within density functional theory as implemented in the full-potential linearized augmented plane-wave (FLAPW) method and mapped to a tight-binding like transport Hamiltonian via non-collinear Wannier functions. The conductance is then computed based on the Landauer formula using the Green's function method. As a first application we study the conductance between two ferromagnetic Co monowires terminated by single Mn apex atoms as a function of Mn-Mn separation. We vary the Mn-Mn separation from the contact (about 2.5 to 5 {\AA}) to the far tunneling regime (5 to 10 {\AA}). The magnetization direction of the Co electrodes is chosen either in parallel or antiparallel alignment and we allow for different spin configurations of the two Mn spins. In the tunneling and into the contact regime the conductance is dominated by $s$-$d_{z^2}$-states. In the close contact regime (below 3.5 {\AA}) there is an additional contribution for a parallel magnetization alignment from the $d_{xz}$- and $d_{yz}$-states which give rise to an increase of the magnetoresistance as it is absent for antiparallel magnetization. If we allow the Mn spins to relax a non-collinear spin state is formed close to contact. We demonstrate that the transition from a collinear to such a non-collinear spin structure as the two Mn atoms approach leaves a characteristic fingerprint in the distance-dependent conductance and magnetoresistance of the junction. We explain the effect of the non-collinear spin state on the conductance based on the spin-dependent hybridization between the $d_{xz,yz}$-states of the Mn spins and their coupling to the Co electrodes.Comment: 13 pages, 5 figure

Equality-friendly well-founded semantics and applications to description logics

We tackle the problem of defining a well-founded semantics (WFS) for Datalog rules with existentially quantified variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog± by non-stratified nonmonotonic nega- tion in rule bodies, and we define a WFS for this generalization via guarded fixed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its profiles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise defi- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering