On Small Beams with Large Topological Charge II: Photons, Electrons and Gravitational Waves

Beams of light with a large topological charge significantly change their spatial structure when they are focused strongly. Physically, it can be explained by an emerging electromagnetic field component in the direction of propagation, which is neglected in the simplified scalar wave picture in optics. Here we ask: Is this a specific photonic behavior, or can similar phenomena also be predicted for other species of particles? We show that the same modification of the spatial structure exists for relativistic electrons as well as for focused gravitational waves. However, this is for different physical reasons: For electrons, which are described by the Dirac equation, the spatial structure changes due to a Spin-Orbit coupling in the relativistic regime. In gravitational waves described with linearized general relativity, the curvature of space-time between the transverse and propagation direction leads to the modification of the spatial structure. Thus, this universal phenomenon exists for both massive and massless elementary particles with Spin 1/2, 1 and 2. It would be very interesting whether other types of particles such as composite systems (neutrons or C$_{60}$) or neutrinos show a similar behaviour and how this phenomenon can be explained in a unified physical way.Comment: 8 pages, 3 figure

Young's experiment and the finiteness of information

Young's experiment is the quintessential quantum experiment. It is argued here that quantum interference is a consequence of the finiteness of information. The observer has the choice whether that information manifests itself as path information or in the interference pattern or in both partially to the extent defined by the finiteness of information.Comment: 5 pages, 3 figures, typos remove

Rethinking affordance

n/a – Critical survey essay retheorising the concept of 'affordance' in digital media context. Lead article in a special issue on the topic, co-edited by the authors for the journal Media Theory

Maximal violation of Clauser-Horne-Shimony-Holt inequality for four-level systems

Clauser-Horne-Shimony-Holt inequality for bipartite systems of 4-dimension is studied in detail by employing the unbiased eight-port beam splitters measurements. The uniform formulae for the maximum and minimum values of this inequality for such measurements are obtained. Based on these formulae, we show that an optimal non-maximally entangled state is about 6% more resistant to noise than the maximally entangled one. We also give the optimal state and the optimal angles which are important for experimental realization.Comment: 7 pages, three table

Maximum Likelihood Methods for Inverse Learning of Optimal Controllers

This paper presents a framework for inverse learning of objective functions for constrained optimal control problems, which is based on the Karush-Kuhn-Tucker (KKT) conditions. We discuss three variants corresponding to different model assumptions and computational complexities. The first method uses a convex relaxation of the KKT conditions and serves as the benchmark. The main contribution of this paper is the proposition of two learning methods that combine the KKT conditions with maximum likelihood estimation. The key benefit of this combination is the systematic treatment of constraints for learning from noisy data with a branch-and-bound algorithm using likelihood arguments. This paper discusses theoretic properties of the learning methods and presents simulation results that highlight the advantages of using the maximum likelihood formulation for learning objective functions.Comment: 21st IFAC World Congres

Age and metallicity gradients in fossil ellipticals

Fossil galaxy groups are speculated to be old and highly evolved systems of galaxies that formed early in the universe and had enough time to deplete their $L^{*}$ galaxies through successive mergers of member galaxies, building up one massive central elliptical, but retaining the group X-ray halo. Considering that fossils are the remnants of mergers in ordinary groups, the merger history of the progenitor group is expected to be imprinted in the fossil central galaxy (FCG). We present for the first time radial gradients of single-stellar population (SSP) ages and metallicites in a sample of FCGs to constrain their formation scenario. Our sample comprises some of the most massive galaxies in the universe exhibiting an average central velocity dispersion of $\sigma_0=271\pm28$ km s$^{-1}$. Metallicity gradients are throughout negative with comparatively flat slopes of $\nabla_{[\rm{Fe/H}]}=- 0.19\pm0.08$ while age gradients are found to be insignificant ($\nabla_{\rm{age}}=0.00\pm0.05$). All FCGs lie on the fundamental plane, suggesting that they are virialised systems. We find that gradient strengths and central metallicities are similar to those found in cluster ellipticals of similar mass. The comparatively flat metallicity gradients with respect to those predicted by monolithic collapse ($\nabla_{Z}=-0.5$) suggest that fossils are indeed the result of multiple major mergers. Hence we conclude that fossils are not 'failed groups' that formed with a top heavy luminosity function. The low scatter of gradient slopes suggests a similar merging history for all galaxies in our sample.Comment: 14 pages, 12 Figures, accepted for publication in A&