Lattice polytopes of degree 2

A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with exactly $i>0$ interior lattice points. We will show that the same bound is true for the normalized volume of lattice polytopes of degree 2 even in higher dimensions. In particular, there is only a finite number of quadratic polynomials with fixed leading coefficient being the $h^*$-polynomial of a lattice polytope.Comment: 8 page

What actually Happens to EU Directives in the Member States? – A Cross-Country Cross-Sector View on National Transposition Instruments

This study empirically investigates the transposition patterns of EU directives in all 15 member states and in six major sectors of the economy with a view on analysing the political-economic reasons behind sector and national differences in the legal transposition instruments used. In particular, we model the influence of both national sector importance and governmental constellations on the ratio of primary to totally transposed EU directives. We find that government strength and net EU receipts negatively affect the ratio of primary to total transpositions. Economic sector size plays a positive significant role for primary transposition ratios. However, the direction of the effect changes if we control for other sector characteristics, i.e. sector lobbying potential and technicality.

Sequential quantum-enhanced measurement with an atomic ensemble

We propose a quantum-enhanced iterative (with $K$ steps) measurement scheme based on an ensemble of $N$ two-level probes which asymptotically approaches the Heisenberg limit $\delta_K \propto R^{-K/(K+1)}$, $R$ the number of quantum resources. The protocol is inspired by Kitaev's phase estimation algorithm and involves only collective manipulation and measurement of the ensemble. The iterative procedure takes the shot-noise limited primary measurement with precision $\delta_1\propto N^{-1/2}$ to increasingly precise results $\delta_K\propto N^{-K/2}$. A straightforward implementation of the algorithm makes use of a two-component atomic cloud of Bosons in the precision measurement of a magnetic field.Comment: 5 pages, 1 figur

Macroscopic Entanglement of a Bose Einstein Condensate on a Superconducting Atom Chip

We propose and analyse a practically implementable scheme to generate macroscopic entanglement of a Bose-Einstein condensate in a micro-magnetic trap magnetically coupled to a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupled with the magnetic trap to generate macroscopic entanglement. Our scheme also provides a platform to realise interferometry of entangled atoms through the Bose-Einstein condensate and to explore physics at the quantum-classical interface.Comment: 4 Pages, Two figure

Light-Mediated Collective Atomic Motion in an Optical Lattice Coupled to a Membrane

We observe effects of collective atomic motion in a one-dimensional optical lattice coupled to an optomechanical system. In this hybrid atom-optomechanical system, the lattice light generates a coupling between the lattice atoms as well as between atoms and a micromechanical membrane oscillator. For large atom numbers we observe an instability in the coupled system, resulting in large-amplitude atom-membrane oscillations. We show that this behavior can be explained by light-mediated collective atomic motion in the lattice, which arises for large atom number, small atom-light detuning and asymmetric pumping of the lattice, in agreement with previous theoretical work. The model connects the optomechanical instability to a phase delay in the global atomic back-action onto the lattice light, which we observe in a direct measurement.Comment: new introduction, title and outlook; small modifications of the main text and figure

What actually happens to EU directives in the member states?: A cross-country cross-sector view on national transposition instruments

This study empirically investigates the transposition patterns of EU directives in all 15 member states and in six major sectors of the economy with a view on analysing the political-economic reasons behind sector and national differences in the legal transposition instruments used. In particular, we model the influence of both national sector importance and governmental constellations on the ratio of primary to totally transposed EU directives. We find that government strength and net EU receipts negatively affect the ratio of primary to total transpositions. Economic sector size plays a positive significant role for primary transposition ratios. However, the direction of the effect changes if we control for other sector characteristics, i.e. sector lobbying potential and technicality

Moritz Cantor: Vorlesungen über Geschichte der Mathematik. Rezensionen von Peter Treutlein im Jahrbuch über die Fortschritte der Mathematik / Zusammengestellt von Gabriele Dörflinger

Der Karlsruher Gymnasialprofessor Peter Treutlein (1845-1912) schrieb ab 1892 sämtliche Rezensionen zu Cantors Mathematikgeschichte im Jahrbuch über die Fortschritte der Mathematik. Im Gegensatz zu den Rezensionen Gustaf Eneströms geht Peter Treutlein nicht auf Einzelheiten ein und weist auch nicht auf Fehler hin. Seine Referate enden in der Regel mit dem Dank an Moritz Cantor

Photon Qubit is Made of Two Colors

Single particles of light can be prepared in a quantum superposition of two different colors, an achievement that could prove useful for quantum information processing

Mesoscopic quantum superpositions in bimodal Bose-Einstein condensates: decoherence and strategies to counteract it

We study theoretically the interaction-induced generation of mesoscopic coherent spin state superpositions (small cat states) from an initial coherent spin state in bimodal Bose-Einstein condensates and the subsequent phase revival, including decoherence due to particle losses and fluctuations of the total particle number. In a full multimode description, we propose a preparation procedure of the initial coherent spin state and we study the effect of preexisting thermal fluctuations on the phase revival, and on the spin and orbito-spinorial cat fidelities.Comment: 26 pages, 12 figures; published versio