Duality of reduced density matrices and their eigenvalues

For states of quantum systems of $N$ particles with harmonic interactions we prove that each reduced density matrix $\rho$ obeys a duality condition. This condition implies duality relations for the eigenvalues $\lambda_k$ of $\rho$ and relates a harmonic model with length scales $l_1,l_2, \ldots, l_N$ with another one with inverse lengths $1/l_1, 1/l_2,\ldots, 1/l_N$. Entanglement entropies and correlation functions inherit duality from $\rho$. Self-duality can only occur for noninteracting particles in an isotropic harmonic trap

Number-parity effect for confined fermions in one dimension

For $N$ spin-polarized fermions with harmonic pair interactions in a $1$-dimensional trap an odd-even effect is found. The spectrum of the $1$-particle reduced density matrix of the system's ground state differs qualitatively for $N$ odd and $N$ even. This effect does only occur for strong attractive and repulsive interactions. Since it does not exists for bosons, it must originate from the repulsive nature implied by the fermionic exchange statistics. In contrast to the spectrum, the $1$-particle density and correlation function for strong attractive interactions do not show any sensitivity on the number parity. This also suggests that reduced-density-matrix-functional theory has a more subtle $N$-dependency than density functional theory.Comment: published versio

Solid-phase microextraction for bioconcentration studies according to OECD TG 305

An important aim of the European Community Regulation on chemicals and their safe use is the identification of (very) persistent, (very) bioaccumulative, and toxic substances. In other regulatory chemical safety assessments (pharmaceuticals, biocides, pesticides), the identification of such (very) persistent, (very) bioaccumulative, and toxic substances is of increasing importance. Solid-phase microextraction is especially capable of extracting total water concentrations as well as the freely dissolved fraction of analytes in the water phase, which is available for bioconcentration in fish. However, although already well established in environmental analyses to determine and quantify analytes mainly in aqueous matrices, solid-phase microextraction is still a rather unusual method in regulatory ecotoxicological research. Here, the potential benefits and drawbacks of solid-phase microextraction are discussed as an analytical routine approach for aquatic bioconcentration studies according to OECD TG 305, with a special focus on the testing of hydrophobic organic compounds characterized by log KOW > 5

Simultaneous observations of haemolymph flow and ventilation in marine spider crabs at different temperatures: a flow weighted MRI study

In vivo magnetic resonance imaging (MRI) and angiography were applied to the marine spider crab Maja squinado for a study of temperature effects and thermal tolerance. Ventilation and haemolymph circulation were investigated during progressive cooling from 12°C to 2°C. The anatomical resolution of MR images from Maja squinado obtained with a standard spin echo sequence were suitable to resolve the structures of various internal organs. The heart of the animal could be depicted without movement artifacts. The use of a flow compensated gradient echo sequence allowed simultaneous observations of ventilation, reflected by water flow through the gill chambers as well as of haemolymph flow. Simultaneous investigation of various arteries was possible by use of flow weighted MRI. In addition to those accessible by standard invasive flow sensitive doppler sensors, flow changes in gill, leg arteries and the venous return could be observed. Both ventilation and haemolymph flow decreased during progressive cooling and changes in haemolymph flow varied between arteries. Haemolymph flow through the Arteria sternalis, some gill and leg arteries was maintained at low temperatures indicating a reduced thermal sensitivity of flow in selected vessels. In support of previous invasive studies of haemolymph flow as well as heart and ventilation rates, the results demonstrate that the operation of gills and the maintenance of locomotor activity are critical for cold tolerance. A shift in haemolymph flow between arteries likely occurs to ensure the functioning of locomotion and ventilation in the cold

Spin-dependent shot noise enhancement in a quantum dot

The spin-dependent dynamical blockade was investigated in a lateral quantum dot in a magnetic field. Spin-polarized edge channels in the two-dimensional leads and the spatial distribution of Landau orbitals in the dot modulate the tunnel coupling of the quantum dot level spectrum. In a measurement of the electron shot noise we observe a pattern of super-Poissonian noise which is correlated to the spin-dependent competition between different transport channels

Parallelism in Constraint Programming

Writing efficient parallel programs is the biggest challenge of the software industry for the foreseeable future. We are currently in a time when parallel computers are the norm, not the exception. Soon, parallel processors will be standard even in cell phones. Without drastic changes in hardware development, all software must be parallelized to its fullest extent. Parallelism can increase performance and reduce power consumption at the same time. Many programs will execute faster on a dual-core processor than a single core processor running at twice the speed. Halving the speed of a processor can reduce the power consumption up to four times. Hence, parallelism gives more performance per unit of power to efficient programs. In order to make use of parallel hardware, we need to overcome the difficulties of parallel programming. To many programmers, it is easier to learn a handful of small domain-specific programming languages than to learn efficient parallel programming. The frameworks for these languages can then automatically parallelize the program. Automatically parallelizing traditional programs is usually much more difficult. In this thesis, we study and present parallelism in constraint programming (CP). We have developed the first constraint framework that automatically parallelizes both the consistency and the search of the solving process. This allows programmers to avoid the difficult issues of parallel programming. We also study distributed CP with independent agents and propose solutions to this problem. Our results show that automatic parallelism in CP can provide very good performance. Our parallel consistency scales very well for problems with many large constraints. We also manage to combine parallel consistency and parallel search with a performance increase. The communication and load-balancing schemes we developed increase the scalability of parallel search. Our model for distributed CP is orders of magnitude faster than traditional approaches. As far as we know, it is the first to solve standard benchmark scheduling problems