A Quantum Lovasz Local Lemma

The Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of "weakly dependent" criteria. We show that the LLL extends to a much more general geometric setting, where events are replaced with subspaces and probability is replaced with relative dimension, which allows to lower bound the dimension of the intersection of vector spaces under certain independence conditions. Our result immediately applies to the k-QSAT problem: For instance we show that any collection of rank 1 projectors with the property that each qubit appears in at most $2^k/(e \cdot k)$ of them, has a joint satisfiable state. We then apply our results to the recently studied model of random k-QSAT. Recent works have shown that the satisfiable region extends up to a density of 1 in the large k limit, where the density is the ratio of projectors to qubits. Using a hybrid approach building on work by Laumann et al. we greatly extend the known satisfiable region for random k-QSAT to a density of $\Omega(2^k/k^2)$. Since our tool allows us to show the existence of joint satisfying states without the need to construct them, we are able to penetrate into regions where the satisfying states are conjectured to be entangled, avoiding the need to construct them, which has limited previous approaches to product states.Comment: 19 page

Very high-energy γ-ray observations of the Crab nebula and other potential sources with the GRAAL experiment

The “γ-ray astronomy at Almeria” (GRAAL) experiment uses 63 heliostat-mirrors with a total mirror area of ≈2500 m2 from the CESA-1 field at the “Plataforma Solar de Almeria” to collect Cherenkov light from air showers. The detector is located in a central solar tower and detects photon-induced showers with an energy threshold of 250±110 GeV and an asymptotic effective detection area of about 15 000 m2. A comparison between the results of detailed Monte-Carlo simulations and data is presented. Data sets taken in the period September 1999–September 2000 in the direction of the Crab pulsar, the active galaxy 3C 454.3, the unidentified γ-ray source 3EG J1835+59 and a “pseudosource” were analyzed for high energy γ-ray emission. Evidence for a γ-ray flux from the Crab pulsar with an integral flux of 2.2±0.4 above threshold and a significance of 4.5σ in a total measuring time of 7 h and 10 min on source was found. No evidence for emission from the other sources was found. Some difficulties with the use of heliostat fields for γ-ray astronomy are pointed out. In particular the effect of field-of-view restricted to the central part of a detected air shower on the lateral distribution and timing properties of Cherenkov light are discussed. Upon restriction the spread of the timing front of proton-induced showers sharply decreases and the reconstructed direction becomes biased towards the pointing direction. This is shown to make efficient γ-hadron separation difficult

Magnons in real materials from density-functional theory

We present an implementation of the adiabatic spin-wave dynamics of Niu and Kleinman. This technique allows to decouple the spin and charge excitations of a many-electron system using a generalization of the adiabatic approximation. The only input for the spin-wave equations of motion are the energies and Berry curvatures of many-electron states describing frozen spin spirals. The latter are computed using a newly developed technique based on constrained density-functional theory, within the local spin density approximation and the pseudo-potential plane-wave method. Calculations for iron show an excellent agreement with experiments.Comment: 1 LaTeX file and 1 postscript figur

Mycoheterotrophic plants living on arbuscular mycorrhizal fungi are generally enriched in ¹³C, ¹⁵N and ²H isotopes

1. Fully mycoheterotrophic plants are thought to obtain carbon exclusively from their root-associated fungal partners. The general enrichment of these plants in the heavy isotopes 13C and 15N suggests that fungi are the main nutrient source for these plants. Yet, the majority of studies have targeted mycoheterotrophic plants associated with ectomycorrhizal, orchid mycorrhizal and saprotrophic fungi, while mycoheterotrophic plants living on arbuscular mycorrhizal fungi remain understudied. 2. Here, we sampled 13 species of arbuscular mycorrhizal fully mycoheterotrophic plants from five families and co-occurring autotrophic reference plants growing in forests of tropical South America, tropical South East Asia and temperate Australasia. We measured stable isotope natural abundances (δ13C, δ15N, δ2H and δ18O), determined total nitrogen concentrations and used high-throughput DNA sequencing to characterize the arbuscular mycorrhizal fungal communities associated with the sampled mycoheterotrophic plants. 3. We observed a general enrichment in 13C and 15N isotopes across mycoheterotrophic plant families and geographic regions. We confirm cases where no 15N enrichment is present, but we show that in general arbuscular mycoheterotrophic plants are enriched in 15N. Moreover, we demonstrate for the first time that these plants are significantly enriched in 2H but not in 18O in relation to their autotrophic references. The fungal communities targeted by the mycoheterotrophs mainly consist of Glomeraceae and show strong association with the isotopic signatures and geographic origin of the plants. 4. Synthesis. Our findings enlarge the limited knowledge on the multi-element stable isotopic signatures of mycoheterotrophic plants living on arbuscular mycorrhizal fungi. We show that these plants are enriched in 13C and 2H as expected due to their mycoheterotrophic nutrition, and that in general they are also enriched in 15N, despite some exceptions. Variation in stable isotope signatures is likely influenced by plant taxonomy, geography and fungal community composition

The GRAAL Project

26th International Cosmic Ray Conference Salt Lake City, Utah August 17-25,1999The GRAAL Project (Gamma Ray Astronomy at ALmeria) makes use of the CESA-1 heliostat field at the “Plataforma Solar de Almeria” (Spain) as a gamma-ray telescope with an energy threshold of about 100 GeV. Cherenkov light generated by EAS is reflected by the heliostats and collected into photomultipliers (PMTs) with nonimaging secondary optics. Each PMT collects the light reflected by 13 - 18 heliostats of 40 m2 using a Winston cone. After successful tests with two collecting cones, a more advanced setup on a dedicated platform, using four collectors and 63 heliostats (total reflecting area of about 2500 m2 ) is being installed. A description of this setup together with Monte Carlo results about its excellent capabilities in the precise determination of pulse arrival times are presented

A new and efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy

Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is given a matrix continued-fraction representation whose coefficients can be obtained from the non-symmetric block-Lanczos method. The resulting algorithm allows for the calculation of the {\em full spectrum} of a system with a computational workload which is only a few times larger than that needed for {\em static} polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with the calculation of the spectrum of benzene, and prospects for its application to the large-scale calculation of optical spectra are discussed.Comment: 4 pages, 2 figure

Detectability of atmospheric features of Earth-like planets in the habitable zone around M dwarfs

We investigate the detectability of atmospheric spectral features of Earth-like planets in the habitable zone (HZ) around M dwarfs with the future James Webb Space Telescope (JWST). We use a coupled 1D climate-chemistry-model to simulate the influence of a range of observed and modelled M-dwarf spectra on Earth-like planets. The simulated atmospheres served as input for the calculation of the transmission spectra of the hypothetical planets, using a line-by-line spectral radiative transfer model. To investigate the spectroscopic detectability of absorption bands with JWST we further developed a signal-to-noise ratio (S/N) model and applied it to our transmission spectra. High abundances of CH$_4$ and H$_2$O in the atmosphere of Earth-like planets around mid to late M dwarfs increase the detectability of the corresponding spectral features compared to early M-dwarf planets. Increased temperatures in the middle atmosphere of mid- to late-type M-dwarf planets expand the atmosphere and further increase the detectability of absorption bands. To detect CH$_4$, H$_2$O, and CO$_2$ in the atmosphere of an Earth-like planet around a mid to late M dwarf observing only one transit with JWST could be enough up to a distance of 4 pc and less than ten transits up to a distance of 10 pc. As a consequence of saturation limits of JWST and less pronounced absorption bands, the detection of spectral features of hypothetical Earth-like planets around most early M dwarfs would require more than ten transits. We identify 276 existing M dwarfs (including GJ 1132, TRAPPIST-1, GJ 1214, and LHS 1140) around which atmospheric absorption features of hypothetical Earth-like planets could be detected by co-adding just a few transits. We show that using transmission spectroscopy, JWST could provide enough precision to be able to partly characterise the atmosphere of Earth-like TESS planets around mid to late M dwarfs.Comment: 18 pages, 10 figure

The extrasolar planet Gliese 581 d: a potentially habitable planet? (Corrigendum to arXiv:1009.5814)

We report here that the equation for H2O Rayleigh scattering was incorrectly stated in the original paper [arXiv:1009.5814]. Instead of a quadratic dependence on refractivity r, we accidentally quoted an r^4 dependence. Since the correct form of the equation was implemented into the model, scientific results are not affected.Comment: accepted to Astronomy&Astrophysic

Chemical trigger toward phase separation in the aqueous Al(III) system revealed

Although Al(III) hydrolysis, condensation, and nucleation play pivotal roles in the synthesis of Al-based compounds and determine their chemical behavior, we still lack experimental evidence regarding the chemistry of nucleation from solution. Here, by combining advanced titration assays, high-resolution transmission electron microscopy (HR-TEM), and 27Al–nuclear magnetic resonance spectroscopy, we show that highly dynamic solute prenucleation clusters (PNCs) are fundamental precursors of nanosolid formation. Chemical changes from olation to oxolation bridging within PNCs rely on the formation of tetrahedral AlO4 in solution and trigger phase separation at low driving force (supersaturation). This does not include the formation of Keggin-Al13 ions, at least during the earliest stages. The PNC pathway of the formation of Al(III) (oxy)(hydr)oxides offers new possibilities toward the development of strategies for controlling the entire crystallization process