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

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

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

A laser gyroscope system to detect the Gravito-Magnetic effect on Earth

Large scale square ring laser gyros with a length of four meters on each side are approaching a sensitivity of 1x10^-11 rad/s/sqrt(Hz). This is about the regime required to measure the gravitomagnetic effect (Lense Thirring) of the Earth. For an ensemble of linearly independent gyros each measurement signal depends upon the orientation of each single axis gyro with respect to the rotational axis of the Earth. Therefore at least 3 gyros are necessary to reconstruct the complete angular orientation of the apparatus. In general, the setup consists of several laser gyroscopes (we would prefer more than 3 for sufficient redundancy), rigidly referenced to each other. Adding more gyros for one plane of observation provides a cross-check against intra-system biases and furthermore has the advantage of improving the signal to noise ratio by the square root of the number of gyros. In this paper we analyze a system of two pairs of identical gyros (twins) with a slightly different orientation with respect to the Earth axis. The twin gyro configuration has several interesting properties. The relative angle can be controlled and provides a useful null measurement. A quadruple twin system could reach a 1% sensitivity after 3:2 years of data, provided each square ring has 6 m length on a side, the system is shot noise limited and there is no source for 1/f- noise.Comment: 9 pages, 6 figures. 2010 Honourable mention of the Gravity Research Foundation; to be published on J. Mod. Phys.

A Zero-Gravity Instrument to Study Low Velocity Collisions of Fragile Particles at Low Temperatures

We discuss the design, operation, and performance of a vacuum setup constructed for use in zero (or reduced) gravity conditions to initiate collisions of fragile millimeter-sized particles at low velocity and temperature. Such particles are typically found in many astronomical settings and in regions of planet formation. The instrument has participated in four parabolic flight campaigns to date, operating for a total of 2.4 hours in reduced gravity conditions and successfully recording over 300 separate collisions of loosely packed dust aggregates and ice samples. The imparted particle velocities achieved range from 0.03-0.28 m s^-1 and a high-speed, high-resolution camera captures the events at 107 frames per second from two viewing angles separated by either 48.8 or 60.0 degrees. The particles can be stored inside the experiment vacuum chamber at temperatures of 80-300 K for several uninterrupted hours using a built-in thermal accumulation system. The copper structure allows cooling down to cryogenic temperatures before commencement of the experiments. Throughout the parabolic flight campaigns, add-ons and modifications have been made, illustrating the instrument flexibility in the study of small particle collisions.Comment: D. M. Salter, D. Hei{\ss}elmann, G. Chaparro, G. van der Wolk, P. Rei{\ss}aus, A. G. Borst, R. W. Dawson, E. de Kuyper, G. Drinkwater, K. Gebauer, M. Hutcheon, H. Linnartz, F. J. Molster, B. Stoll, P. C. van der Tuijn, H. J. Fraser, and J. Blu

Long-term validation of Aeolus L2B wind products at Punta Arenas, Chile, and Leipzig, Germany

Ground-based observations of horizontal winds have been performed at Leipzig (51.35∘ N, 12.43∘ E), Germany, and at Punta Arenas (53.15∘ S, 70.91∘ W), Chile, in the framework of the German initiative EVAA (Experimental Validation and Assimilation of Aeolus observations) with respect to the validation of the Mie and Rayleigh wind products of Aeolus (L2B data). In Leipzig, at the Leibniz Institute for Tropospheric Research (TROPOS), radiosondes have been launched for the Aeolus overpasses on each Friday (ascending orbit) since the middle of May 2019. In Punta Arenas, scanning Doppler cloud radar observations have been performed in the framework of the DACAPO-PESO campaign (dacapo.tropos.de) for more than 3 years from the end of 2018 until the end of 2021 and could be used to validate Aeolus measurements on its ascending and descending orbits. We present two case studies and long‐term statistics of the horizontal winds derived with the ground-based reference instruments compared to Aeolus horizontal line-of-sight (HLOS) winds. The wind products of Aeolus considered are the Mie cloudy and Rayleigh clear products. It was found that the deviation of the Aeolus HLOS winds from the ground reference is usually of Gaussian shape, which allowed the use of the median bias and the scaled median absolute deviation (MAD) for the determination of the systematic and random errors of Aeolus wind products, respectively. The case study from August 2020 with impressive atmospheric conditions at Punta Arenas shows that Aeolus is able to capture strong wind speeds of up to more than 100 m s−1. The long-term validation was performed in Punta Arenas covering the period from December 2018 to November 2021 and in Leipzig from May 2019 until September 2022. This analysis showed that the systematic error of the Aeolus wind products could be significantly lowered during the mission lifetime with the changes introduced into the processing chain (different versions are called baselines). While in the early mission phase, systematic errors of more than 2 m s−1 (absolute values) were observed for both wind types (Mie and Rayleigh), these biases could be reduced with the algorithm improvements, such as the introduction of the correction for temperature fluctuations at the main telescope of Aeolus (M1 temperature correction) with Baseline 09. Hence, since Baseline 10, a significant improvement in the Aeolus data was found, leading to a low systematic error (close to 0 m s−1) and similar values for the midlatitudinal sites in both hemispheres. The random errors for both wind products were first decreasing with an increasing baseline but later increasing again due to performance losses of the Aeolus lidar instrument. Nevertheless, no significant increase in the systematic error in the Aeolus wind products was found. Thus, one can conclude that the uncertainty introduced by the reduced atmospheric return signal received by Aeolus mostly affects the random error. Even when considering all the challenges during the mission, we can confirm the general validity of Aeolus observations during its lifetime. Therefore, this space explorer mission could demonstrate that it is possible to perform active wind observations from space with the applied technique.</p

Smartspectrometer—embedded optical spectroscopy for applications in agriculture and industry

The ongoing digitization of industry and agriculture can benefit significantly from optical spectroscopy. In many cases, optical spectroscopy enables the estimation of properties such as substance concentrations and compositions. Spectral data can be acquired and evaluated in real time, and the results can be integrated directly into process and automation units, saving resources and costs. Multivariate data analysis is needed to integrate optical spectrometers as sensors. Therefore, a spectrometer with integrated artificial intelligence (AI) called SmartSpectrometer and its interface is presented. The advantages of the SmartSpectrometer are exemplified by its integration into a harvesting vehicle, where quality is determined by predicting sugar and acid in grapes in the field

Control over phase separation and nucleation using a laser-tweezing potential

Control over the nucleation of new phases is highly desirable but elusive. Even though there is a long history of crystallization engineering by varying physicochemical parameters, controlling which polymorph crystallizes or whether a molecule crystallizes or forms an amorphous precipitate is still a poorly understood practice. Although there are now numerous examples of control using laser-induced nucleation, the absence of physical understanding is preventing progress. Here we show that the proximity of a liquid–liquid critical point or the corresponding binodal line can be used by a laser-tweezing potential to induce concentration gradients. A simple theoretical model shows that the stored electromagnetic energy of the laser beam produces a free-energy potential that forces phase separation or triggers the nucleation of a new phase. Experiments in a liquid mixture using a low-power laser diode confirm the effect. Phase separation and nucleation using a laser-tweezing potential explains the physics behind non-photochemical laser-induced nucleation and suggests new ways of manipulating matter