Visualization and comparison of classical structures and quantum states of 4D maps

For generic 4D symplectic maps we propose the use of 3D phase-space slices which allow for the global visualization of the geometrical organization and coexistence of regular and chaotic motion. As an example we consider two coupled standard maps. The advantages of the 3D phase-space slices are presented in comparison to standard methods like 3D projections of orbits, the frequency analysis, and a chaos indicator. Quantum mechanically, the 3D phase-space slices allow for the first comparison of Husimi functions of eigenstates of 4D maps with classical phase space structures. This confirms the semi-classical eigenfunction hypothesis for 4D maps.Comment: For videos with rotated view of the 3D phase-space slices in high resolution see http://www.comp-phys.tu-dresden.de/supp

A strictly commutative model for the cochain algebra of a space

The commutative differential graded algebra $A_{\mathrm{PL}}(X)$ of polynomial forms on a simplicial set $X$ is a crucial tool in rational homotopy theory. In this note, we construct an integral version $A^{\mathcal{I}}(X)$ of $A_{\mathrm{PL}}(X)$. Our approach uses diagrams of chain complexes indexed by the category of finite sets and injections $\mathcal{I}$ to model $E_{\infty}$ differential graded algebras by strictly commutative objects, called commutative $\mathcal{I}$-dgas. We define a functor $A^{\mathcal{I}}$ from simplicial sets to commutative $\mathcal{I}$-dgas and show that it is a commutative lift of the usual cochain algebra functor. In particular, it gives rise to a new construction of the $E_{\infty}$ dga of cochains. The functor $A^{\mathcal{I}}$ shares many properties of $A_{\mathrm{PL}}$, and can be viewed as a generalization of $A_{\mathrm{PL}}$ that works over arbitrary commutative ground rings. Working over the integers, a theorem by Mandell implies that $A^{\mathcal{I}}(X)$ determines the homotopy type of $X$ when $X$ is a nilpotent space of finite type.Comment: v3: 23 pages; corrected an error in Lemma 3.7, adjusted some model structures accordingly and made various other small improvement

Fundamental absorption edges in heteroepitaxial YBiO3 thin films

The dielectric function of heteroepitaxial YBiO3 grown on a-Al2O3 single crystals via pulsed laser deposition is determined in the spectral range from 0.03 eV to 4.5 eV by a simultaneous modeling of the spectroscopic ellipsometry and optical transmission data of YBiO3 films of different thicknesses. The (111)-oriented YBiO3 films are nominally unstrained and crystallize in a defective fluorite-type structure with a Fm3⎯⎯m space group. From the calculated absorption spectrum, a direct electronic bandgap energy of 3.6(1) eV and the signature of an indirect electronic transition around 0.5 eV are obtained. These values provide necessary experimental feedback to previous conflicting electronic band structure calculations predicting either a topologically trivial or a non-trivial insulating ground state in YBiO3

Handlungsgrundlage zur Bedarfsanerkennung von Düngemaßnahmen gemäß Anhang I und II der Verordnung (EWG) Nr. 2092/91 über den ökologischen Landbau

In den Erzeugervorschriften der Verordnung (EWG) Nr. 2092/91 sind lediglich Rahmenbedingungen festgelegt worden für die Bedarfsanerkennung von Düngungsmaßnahmen auf dem Öko-Betrieb. Als Ergebnis eines längeren Diskussionsprozesses wurde nachfolgende Handlungsgrundlage für Landwirte und Kontrollstellen des Ökologischen Landbaus zur Bedarfsanerkennung von Düngungsmaßnahmen gemäß Anhang I und II der Verordnung erstellt. In den Handlungsvorgaben und einem Leitfaden werden die fachlichen Grundlagen aufgeführt, so dass eine Entscheidungsfindung zur Bedarfsanerkennung von Düngungsmaßnahmen erleichtert wird