Induced decay of the neutral vaccum in overcritical fields occurring in heavy-ion collisions

In critical or nearly critical heavy-ion collisions, induced as well as spontaneous energyless e-e+ pair creation result in the decay of the neutral vacuum. Induced transitions from the negative-energy continuum into a vacant molecular 1s level can occur even in the absence of diving and produce a substantial enhancement and broadening of the previously considered spontaneous positron spectrum. Total cross sections of 5 b have been calculated for U-U collisions

Solution of the Dirac equation for strong external fields

The 1s bound state of superheavy atoms and molecules reaches a binding energy of -2mc2 at Z≈169. It is shown that the K shell is still localized in r space even beyond this critical proton number and that it has a width Γ (several keV large) which is a positron escape width for ionized K shells. The suggestion is made that this effect can be observed in the collision of very heavy ions (superheavy molecules) during the collision

The exponent in the orthogonality catastrophe for Fermi gases

We quantify the asymptotic vanishing of the ground-state overlap of two non-interacting Fermi gases in $d$-dimensional Euclidean space in the thermodynamic limit. Given two one-particle Schr\"odinger operators in finite-volume which differ by a compactly supported bounded potential, we prove a power-law upper bound on the ground-state overlap of the corresponding non-interacting $N$-particle systems. We interpret the decay exponent $\gamma$ in terms of scattering theory and find $\gamma = \pi^{-2}{\lVert\arcsin{\lvert T_E/2\rvert}\rVert}_{\mathrm{HS}}^2$, where $T_E$ is the transition matrix at the Fermi energy $E$. This exponent reduces to the one predicted by Anderson [Phys. Rev. 164, 352-359 (1967)] for the exact asymptotics in the special case of a repulsive point-like perturbation.Comment: Version as to appear in J. Spectr. Theory, References update

Spin correlation functions in random-exchange s=1/2 XXZ chains

The decay of (disorder-averaged) static spin correlation functions at T=0 for the one-dimensional spin-1/2 XXZ antiferromagnet with uniform longitudinal coupling $J\Delta$ and random transverse coupling $J\lambda_i$ is investigated by numerical calculations for ensembles of finite chains. At $\Delta=0$ (XX model) the calculation is based on the Jordan-Wigner mapping to free lattice fermions for chains with up to N=100 sites. At $\Delta \neq 0$ Lanczos diagonalizations are carried out for chains with up to N=22 sites. The longitudinal correlation function is found to exhibit a power-law decay with an exponent that varies with $\Delta$ and, for nonzero $\Delta$, also with the width of the $\lambda_i$-distribution. The results for the transverse correlation function show a crossover from power-law decay to exponential decay as the exchange disorder is turned on.Comment: RevTex manuscript (7 pages), 4 postscript figure

SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels

We present Spline-based Convolutional Neural Networks (SplineCNNs), a variant of deep neural networks for irregular structured and geometric input, e.g., graphs or meshes. Our main contribution is a novel convolution operator based on B-splines, that makes the computation time independent from the kernel size due to the local support property of the B-spline basis functions. As a result, we obtain a generalization of the traditional CNN convolution operator by using continuous kernel functions parametrized by a fixed number of trainable weights. In contrast to related approaches that filter in the spectral domain, the proposed method aggregates features purely in the spatial domain. In addition, SplineCNN allows entire end-to-end training of deep architectures, using only the geometric structure as input, instead of handcrafted feature descriptors. For validation, we apply our method on tasks from the fields of image graph classification, shape correspondence and graph node classification, and show that it outperforms or pars state-of-the-art approaches while being significantly faster and having favorable properties like domain-independence.Comment: Presented at CVPR 201

Das Alter der Sinterkalke vom Solbad Laer i.T.W.

Aus 4 Profilen durch den Laerer Sinterkalk wurden 33 Proben pollenanalytisch untersucht. Zwei Zähltabellen geben für jede einzelne dieser Proben den Gehalt an Pollen und Sporen. Zwei Diagramme stellen die Ergebnisse dieser qualitativen und quantitativen Analysen graphisch dar. Neben den Pollenkörnern der gebräuchlichen 11 Baumarten wurden 24 verschiedene Nichtbaumpollen-Gruppen ausgewertet. Als ältester Zeitabschnitt ließ sich die mindestens 10000 Jahre alte sog. "Jüngste Dryaszeit" feststellen, gekennzeichnet durch eine subarktische Tundra. Die darauf folgenden Zeitabschnitte Präboreal, Boreal, Atlantikum, Subboreal und Subatlantikum konnten in einem oder mehreren der Profile gefaßt werden. In günstig gelagerten Fällen wurden darüber hinaus Beziehungen angedeutet, die zwischen der Bildung dieses Sinterkalklagers und der Besiedlung durch den Menschen bestehen