Quartic Forms in Many Variables

We show that a quartic $p$-adic form with at least $3192$ variables possesses a non-trivial zero. We also prove new results on systems of cubic, quadratic and linear forms. As an example, we show that for a system comprising two cubic forms $132$ variables are sufficient.Comment: 8 page

pp-adic Zeros of Quintic Forms

It is shown that a quintic form over a p-adic field with at least 26 variables has a non-trivial zero, providing that the cardinality of the residue class field exceeds 9.Comment: Minor correction

Superfluid qubit systems with ring shaped optical lattices

We study an experimentally feasible qubit system employing neutral atomic currents. Our system is based on bosonic cold atoms trapped in ring-shaped optical lattice potentials. The lattice makes the system strictly one dimensional and it provides the infrastructure to realize a tunable ring-ring interaction. Our implementation combines the low decoherence rates of of neutral cold atoms systems, overcoming single site addressing, with the robustness of topologically protected solid state Josephson flux qubits. Characteristic fluctuations in the magnetic fields affecting Josephson junction based flux qubits are expected to be minimized employing neutral atoms as flux carriers. By breaking the Galilean invariance we demonstrate how atomic currents through the lattice provide a implementation of a qubit. This is realized either by artificially creating a phase slip in a single ring, or by tunnel coupling of two homogeneous ring lattices. The single qubit infrastructure is experimentally investigated with tailored optical potentials. Indeed, we have experimentally realized scaled ring-lattice potentials that could host, in principle, $n\sim 10$ of such ring-qubits, arranged in a stack configuration, along the laser beam propagation axis. An experimentally viable scheme of the two-ring-qubit is discussed, as well. Based on our analysis, we provide protocols to initialize, address, and read-out the qubit.Comment: 14 revtex4-1 pages, 7 figs; to be published in Scientific Report

The EU in Times of COVID-19: Together into a Future Based on (More) Solidarity?

The outbreak of the COVID-19-pandemic in spring 2020 put solidarity within the European Union to the test and called for far-reaching responses by all member states to mitigate the pandemic’s effects. But how does this crisis affect public support for transnational solidarity in the European Union? Are EU citizens willing to collectively overcome a financial crisis caused by the COVID-19-pandemic? And what is the public opinion on the establishment of a fictional EU-wide fund to mitigate future crises? Those questions have been addressed by a multi-country survey run by the ‘Solikris’-project. A resulting analysis in the project’s Policy Brief #5 shows that particularly the macroeconomic differences between countries correlate with attitudes towards solidarity policies and that transnational solidarity is higher in situations of acute crisis.Der Ausbruch der COVID-19-Pandemie im Frühjahr 2020 stellte die Solidarität innerhalb der Europäischen Union auf die Probe und erforderte weitreichende Reaktionen aller Mitgliedsstaaten, um die Auswirkungen der Pandemie zu mildern. Doch wie wirkt sich diese Krise auf die öffentliche Unterstützung für transnationale Solidarität in der Europäischen Union aus? Sind die EU-Bürger*innen bereit, eine durch die COVID-19-Pandemie verursachte Finanzkrise kollektiv zu bewältigen? Und wie ist die öffentliche Meinung zur Einrichtung eines fiktiven EU-weiten Fonds zur Abfederung zukünftiger Krisen? Diese Fragen wurden in einer länderübergreifenden Umfrage des ‘Solikris’-Projekts untersucht. Eine daraus resultierende Analyse im Policy Brief #5 des Projekts zeigt, dass insbesondere die makroökonomischen Unterschiede zwischen den Ländern mit den Einstellungen zur Solidaritätspolitik korrelieren und dass die transnationale Solidarität in akuten Krisensituationen höher is

Economic inequality and industrialization on the continent: introductory comments

In dem Beitrag werden einführende Überlegungen zum Problem der Einkommensungleichheit und der Industrialisierung auf dem europäischen Kontinent vorgestellt. Es wird begründet, warum eine Geschichte der Einkommensungleichheit während der Industrialisierung geschrieben werden sollte. Dabei werden folgende Fragen angesprochen: Kann das Modell der 'sozialen Frage' in den historischen Erfahrungen Kontinentaleuropas gefunden werden? Gibt es signifikante Unterschiede zwischen den US-amerikanischen und den britischen Erfahrungen? Welche Art von Daten und Ungleichheits-Indikatoren ist verfügbar für die Analyse? Gibt es eine systematische Beziehung zwischen den Trends regionaler und nationaler Ungleichheiten? Wie sehen die Ursachen und Konsequenzen wirtschaftlicher Ungleichheit aus? Dazu werden verschiedene Forschungsansätze vorgestellt. (KW

Coherence Properties of Guided-Atom Interferometers

We present a detailed investigation of the coherence properties of beam splitters and Mach-Zehnder interferometers for guided atoms. It is demonstrated that such a setup permits coherent wave packet splitting and leads to the appearance of interference fringes. We study single-mode and thermal input states and show that even for thermal input states interference fringes can be clearly observed, thus demonstrating the multimode operation and the robustness of the interferometer.Comment: 4 pages, 4 figure

Interferometer-Type Structures for Guided Atoms

We experimentally demonstrate interferometer-type guiding structures for neutral atoms based on dipole potentials created by micro-fabricated optical systems. As a central element we use an array of atom waveguides being formed by focusing a red-detuned laser beam with an array of cylindrical microlenses. Combining two of these arrays, we realize X-shaped beam splitters and more complex systems like the geometries for Mach-Zehnder and Michelson-type interferometers for atoms.Comment: 4 pages, 6 figure

Three-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Foreground Polarization

We present a full-sky model of polarized Galactic microwave emission based on three years of observations by the Wilkinson Microwave Anisotropy Probe (WMAP) at frequencies from 23 to 94 GHz. The model compares maps of the Stokes Q and U components from each of the 5 WMAP frequency bands in order to separate synchrotron from dust emission, taking into account the spatial and frequency dependence of the synchrotron and dust components. This simple two-component model of the interstellar medium accounts for at least 97% of the polarized emission in the WMAP maps of the microwave sky. Synchrotron emission dominates the polarized foregrounds at frequencies below 50 GHz, and is comparable to the dust contribution at 65 GHz. The spectral index of the synchrotron component, derived solely from polarization data, is -3.2 averaged over the full sky, with a modestly flatter index on the Galactic plane. The synchrotron emission has mean polarization fraction 2--4% in the Galactic plane and rising to over 20% at high latitude, with prominent features such as the North Galactic Spur more polarized than the diffuse component. Thermal dust emission has polarization fraction 1% near the Galactic center, rising to 6% at the anti-center. Diffuse emission from high-latitude dust is also polarized with mean fractional polarization 0.036 +/- 0.011.Comment: 9 pages with 8 figures. For higher quality figures, see the version posted at http://lambda.gsfc.nasa.gov/product/map/dr2/map_bibliography.cf

Polarisation properties of Milky-Way-like galaxies

(Abridged) We study the polarisation properties, magnetic field strength, and synchrotron emission scale-height of Milky-Way-like galaxies in comparison with other spiral galaxies. We use our 3D-emission model of the Milky Way Galaxy for viewing the Milky Way from outside at various inclinations as spiral galaxies are observed. When seen edge-on the synchrotron emission from the Milky Way has an exponential scale-height of about 0.74 kpc, which is much smaller than the values obtained from previous models. We find that current analysis methods overestimate the scale-height of synchrotron emission of galaxies by about 10% at an inclination of 80 degree and about 40% at an inclination of 70 degree because of contamination from the disk. The observed RMs for face-on galaxies derived from high-frequency polarisation measurements approximate to the Faraday depths (FDs) when scaled by a factor of two. For edge-on galaxies, the observed RMs are indicative of the orientation of the large-scale magnetic field, but are not well related with the FDs. Assuming energy equipartition between the magnetic field and particles for the Milky Way results in an average magnetic-field strength, which is about two times larger than the intrinsic value for a K factor of 100. The number distribution of the integrated polarisation percentages of a large sample of unresolved Milky-Way-like galaxies peaks at about 4.2% at 4.8 GHz and at about 0.8% at 1.4GHz. Integrated polarisation angles rotated by 90 degree align very well with the position angles of the major axes, implying that unresolved galaxies do not have intrinsic RMs.Comment: 10 pages, 11 figures, accepted for publication in A&

12CO(J=2->1) and CO(J=3->2) observations of Virgo Cluster spiral galaxies with the KOSMA telescope: global properties

We present 12CO(J=2->1) and CO(J=3->2) observations of quiescent Virgo Cluster spiral galaxies with the KOSMA 3m submm telescope. The beam sizes of 80" at 345 GHz and 120" at 230 GHz are well suited for the investigation of global properties of Virgo Cluster galaxies. The observed sample was selected based on previous 12CO(J=1->0) detections by Stark et al. (1986), performed with the AT&T Bell Laboratory 7m telescope (beam size 100"). We were able to detect 18 spiral galaxies in 12CO(2->1) and 16 in 12CO(3->2). Beam matched observations of the lowest three 12CO transitions allow us to compare our results with previous high spatial resolution studies of (moderate) starburst galaxies and galactic core regions. We discuss the global excitation conditions of the ISM in these quiescent spiral galaxies. The resulting CO (3--2)/(1--0) integrated line ratios vary over a relatively narrow range of values from 0.35 to 0.14 (on a K km/s-scale) with increasing CO (2--1)/(1--0) ratio (from 0.5 to 1.1). The line ratios between the three lowest rotational transitions of CO cannot be fitted by any radiative transfer model with a single source component. A two-component model, assuming a warm, dense nuclear and a cold, less dense disc component allows us to fit the observed line ratios for most of the galaxies individually by selecting suitable parameters. The two-component model, however, fails to explain the observed correlation of the line ratios. This is due to a variation of the relative filling factor of the warm gas alone, assuming a typical set of parameters for the two components common for all galaxies.Comment: accepted for publication in A&A, 9 pages, 8 figure