Time-dependent density-functional theory beyond the adiabatic approximation: insights from a two-electron model system

Most applications of time-dependent density-functional theory (TDDFT) use the adiabatic local-density approximation (ALDA) for the dynamical exchange-correlation potential Vxc(r,t). An exact (i.e., nonadiabatic) extension of the ground-state LDA into the dynamical regime leads to a Vxc(r,t) with a memory, which causes the electron dynamics to become dissipative. To illustrate and explain this nonadiabatic behavior, this paper studies the dynamics of two interacting electrons on a two-dimensional quantum strip of finite size, comparing TDDFT within and beyond the ALDA with numerical solutions of the two-electron time-dependent Schroedinger equation. It is shown explicitly how dissipation arises through multiple particle-hole excitations, and how the nonadiabatic extension of the ALDA fails for finite systems, but becomes correct in the thermodynamic limit.Comment: 10 pages, 7 figure

Hopf Categories

We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We generalize the fundamental theorem for Hopf modules and some of its applications to Hopf categories.Comment: 47 pages; final version to appear in Algebras and Representation Theor

p3d: a general data-reduction tool for fiber-fed integral-field spectrographs

The reduction of integral-field spectrograph (IFS) data is demanding work. Many repetitive operations are required in order to convert raw data into, typically a large number of, spectra. This effort can be markedly simplified through the use of a tool or pipeline, which is designed to complete many of the repetitive operations without human interaction. Here we present our semi-automatic data-reduction tool p3d that is designed to be used with fiber-fed IFSs. Important components of p3d include a novel algorithm for automatic finding and tracing of spectra on the detector, and two methods of optimal spectrum extraction in addition to standard aperture extraction. p3d also provides tools to combine several images, perform wavelength calibration and flat field data. p3d is at the moment configured for four IFSs. In order to evaluate its performance we have tested the different components of the tool. For these tests we used both simulated and observational data. We demonstrate that for three of the IFSs a correction for so-called cross-talk due to overlapping spectra on the detector is required. Without such a correction spectra will be inaccurate, in particular if there is a significant intensity gradient across the object. Our tests showed that p3d is able to produce accurate results. p3d is a highly general and freely available tool. It is easily extended to include improved algorithms, new visualization tools and support for additional instruments. The program code can be downloaded from the p3d-project web site http://p3d.sourceforge.netComment: 18 pages, 15 figures, 3 tables, accepted for publication in A&

Imaging of microwave fields using ultracold atoms

We report a technique that uses clouds of ultracold atoms as sensitive, tunable, and non-invasive probes for microwave field imaging with micrometer spatial resolution. The microwave magnetic field components drive Rabi oscillations on atomic hyperfine transitions whose frequency can be tuned with a static magnetic field. Readout is accomplished using state-selective absorption imaging. Quantitative data extraction is simple and it is possible to reconstruct the distribution of microwave magnetic field amplitudes and phases. While we demonstrate 2d imaging, an extension to 3d imaging is straightforward. We use the method to determine the microwave near-field distribution around a coplanar waveguide integrated on an atom chip.Comment: 11 pages, 4 figure

Methoden zur Verbesserung der Vegetationszusammensetzung in ökologisch bewirtschaftetem Dauergrünland

In der ökologischen Grünlandbewirtschaftung werden artenreiche Bestände mit Standort angepassten und möglichst wertvollen Futterarten angestrebt. Dennoch sind in der Praxis oftmals stark Weidelgras betonte Bestände anzutreffen. Im Vergleich zur Neuansaat sind Nachsaaten deutlich kostengünstiger. Daher wurden im Sommer 2007 auf 8 ökologisch bewirtschafteten Betrieben Nord-Westdeutschlands Nachsaatversuche mit unterschiedlicher Technik (Schlitzsaat und Bandfrässaat) und ausgewählten Arten angelegt. Hierbei würden 5 Gramineen (Lolium perenne, Phleum pratense, Festuca rubra, Dactylis glomerata) und auf drei Standorten in Niedersachsen zusätzlich Festulolium, eine Neuzüchtung aus Festuca- und Lolium-Gattungen sowie eine Futterleguminose (Lotus corniculatus) geprüft. Deutsches Weidelgras und Wiesenlieschgras, aber auch Wiesenschweidel ließen sich mit beiden Nachsaatverfahren meistens gut etablieren. Durch die stark Narben schädigende Bandfrässaat lassen sich auch konkurrenzschwächere Arten wie Knaulgras, Rotschwingel und sogar Hornklee nachhaltig etablieren. Voraussetzung für dauerhaft erfolgreiche Nachsaaten sind eine ausreichende Wasser- und Nährstoffverfügbarkeit sowie allgemein günstige Standortbedingungen. Die besten Ergebnisse wurden mit der Bandfrässaat auf den sandigeren Standorten, während das Frässaatverfahren für schwere Marsch- und Tonböden nur bedingt geeignet ist, weil die Bodenstruktur unter ungünstigen Bedingungen zu stark geschädigt wird

Complex collective states in a one-dimensional two-atom system

We consider a pair of identical two-level atoms interacting with a scalar field in one dimension, separated by a distance $x_{21}$. We restrict our attention to states where one atom is excited and the other is in the ground state, in symmetric or anti-symmetric combinations. We obtain exact collective decaying states, belonging to a complex spectral representation of the Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and the real parts give the average energy of the collective states. In one dimension there is strong interference between the fields emitted by the atoms, leading to long-range cooperative effects. The decay rates and the energy oscillate with the distance $x_{21}$. Depending on $x_{21}$, the decay rates will either decrease, vanish or increase as compared with the one-atom decay rate. We have sub- and super-radiance at periodic intervals. Our model may be used to study two-cavity electron wave-guides. The vanishing of the collective decay rates then suggests the possibility of obtaining stable configurations, where an electron is trapped inside the two cavities.Comment: 14 pages, 14 figures, submitted to Phys. Rev.