Better Answers to Real Questions

We consider existential problems over the reals. Extended quantifier elimination generalizes the concept of regular quantifier elimination by providing in addition answers, which are descriptions of possible assignments for the quantified variables. Implementations of extended quantifier elimination via virtual substitution have been successfully applied to various problems in science and engineering. So far, the answers produced by these implementations included infinitesimal and infinite numbers, which are hard to interpret in practice. We introduce here a post-processing procedure to convert, for fixed parameters, all answers into standard real numbers. The relevance of our procedure is demonstrated by application of our implementation to various examples from the literature, where it significantly improves the quality of the results

Neutrino-driven supernova of a low-mass iron-core progenitor boosted by three-dimensional turbulent convection

We present the first successful simulation of a neutrino-driven supernova explosion in three dimensions (3D), using the Prometheus-Vertex code with an axis-free Yin-Yang grid and a sophisticated treatment of three-flavor, energy-dependent neutrino transport. The progenitor is a nonrotating, zero-metallicity 9.6 Msun star with an iron core. While in spherical symmetry outward shock acceleration sets in later than 300 ms after bounce, a successful explosion starts at ~130 ms postbounce in two dimensions (2D). The 3D model explodes at about the same time but with faster shock expansion than in 2D and a more quickly increasing and roughly 10 percent higher explosion energy of >10^50 erg. The more favorable explosion conditions in 3D are explained by lower temperatures and thus reduced neutrino emission in the cooling layer below the gain radius. This moves the gain radius inward and leads to a bigger mass in the gain layer, whose larger recombination energy boosts the explosion energy in 3D. These differences are caused by less coherent, less massive, and less rapid convective downdrafts associated with postshock convection in 3D. The less violent impact of these accretion downflows in the cooling layer produces less shock heating and therefore diminishes energy losses by neutrino emission. We thus have, for the first time, identified a reduced mass accretion rate, lower infall velocities, and a smaller surface filling factor of convective downdrafts as consequences of 3D postshock turbulence that facilitate neutrino-driven explosions and strengthen them compared to the 2D case.Comment: 7 pages, 5 figures; revised version with more discussion of resolution dependence and differences to other 3D results; accepted by ApJ

Concurrence of mixed multi-partite quantum states

We propose generalizations of concurrence for multi-partite quantum systems that can distinguish qualitatively distinct quantum correlations. All introduced quantities can be evaluated efficiently for arbitrary mixed sates

Measures and dynamics of entangled states

We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for different, realistic experimental scenarios.Comment: Physics Reports, in pres

Fast time variations of supernova neutrino fluxes and their detectability

In the delayed explosion scenario of core-collapse supernovae (SNe), the accretion phase shows pronounced convective overturns and a low-multipole hydrodynamic instability, the standing accretion shock instability (SASI). These effects imprint detectable fast time variations on the emerging neutrino flux. Among existing detectors, IceCube is best suited to this task, providing an event rate of ~1000 events per ms during the accretion phase for a fiducial SN distance of 10 kpc, comparable to what could be achieved with a megaton water Cherenkov detector. If the SASI activity lasts for several hundred ms, a Fourier component with an amplitude of 1% of the average signal clearly sticks out from the shot noise. We analyze in detail the output of axially symmetric hydrodynamical simulations that predict much larger amplitudes up to frequencies of a few hundred Hz. If these models are roughly representative for realistic SNe, fast time variations of the neutrino signal are easily detectable in IceCube or future megaton-class instruments. We also discuss the information that could be deduced from such a measurement about the physics in the SN core and the explosion mechanism of the SN.Comment: 14 pages, 11 figures. Final version accepted in PRD. Section on astrophysical relevance and several references adde

Erratum: Progenitor-explosion connection and remnant birth masses for neutrino-driven supernovae of iron-core progenitors (2012, ApJ, 757, 69)

An erroneous interpretation of the hydrodynamical results led to an incorrect determination of the fallback masses in Ugliano et al. (2012), which also (on a smaller level) affects the neutron star masses provided in that paper. This problem was already addressed and corrected in the follow-up works by Ertl et al. (2015) and Sukhbold et al. (2015). Therefore, the reader is advised to use the new data of the latter two publications. In the remaining text of this Erratum we present the differences of the old and new fallback results in detail and explain the origin of the mistake in the original analysis by Ugliano et al. (2012).Comment: 3 pages, 2 figures; submitted to The Astrophysical Journa

Magneto-optical probing of weak disorder in a two-dimensional hole gas

In two-beam magneto-photoluminescence spectra of a two-dimensional valence hole gas we identify the three-level energy spectrum of a free positive trion with a field-induced singlet-triplet transition. The recombination spectrum of acceptor-bound trions is also detected, including a cyclotron replica corresponding to the hole shake-up process. The emergence of a shake-up peak at low temperature is shown to be a sensitive probe of the presence of a small number of impurities inside the high-mobility quantum well, and its relative position is directly related to the hole cyclotron mass.Comment: 4 pages, 5 figure

Core-Collapse Supernovae: Reflections and Directions

Core-collapse supernovae are among the most fascinating phenomena in astrophysics and provide a formidable challenge for theoretical investigation. They mark the spectacular end of the lives of massive stars and, in an explosive eruption, release as much energy as the sun produces during its whole life. A better understanding of the astrophysical role of supernovae as birth sites of neutron stars, black holes, and heavy chemical elements, and more reliable predictions of the observable signals from stellar death events are tightly linked to the solution of the long-standing puzzle how collapsing stars achieve to explode. In this article our current knowledge of the processes that contribute to the success of the explosion mechanism are concisely reviewed. After a short overview of the sequence of stages of stellar core-collapse events, the general properties of the progenitor-dependent neutrino emission will be briefly described. Applying sophisticated neutrino transport in axisymmetric (2D) simulations with general relativity as well as in simulations with an approximate treatment of relativistic effects, we could find successful neutrino-driven explosions for a growing set of progenitor stars. First results of three-dimensional (3D) models have been obtained, and magnetohydrodynamic simulations demonstrate that strong initial magnetic fields in the pre-collapse core can foster the onset of neutrino-powered supernova explosions even in nonrotating stars. These results are discussed in the context of the present controversy about the value of 2D simulations for exploring the supernova mechanism in realistic 3D environments, and they are interpreted against the background of the current disagreement on the question whether the standing accretion shock instability (SASI) or neutrino-driven convection is the crucial agency that supports the onset of the explosion.Comment: 36 pages, 20 figures (43 eps files); submitted to Progress of Theoretical and Experimental Physics (PTEP