Circular polarization reversal of half-vortex cores in polariton condensates

Vortices are topological objects carrying quantized orbital angular momentum and have been widely studied in many physical systems for their applicability in information storage and processing. In systems with spin degree of freedom the elementary excitations are so called half-vortices, carrying a quantum rotation only in one of the two spin components. We study the spontaneous formation and stability of localized such half-vortices in semiconductor microcavity polariton condensates, non-resonantly excited by a linearly polarized ring-shaped pump. The TE-TM splitting of optical modes in the microcavity system leads to an effective spin-orbit coupling, resulting in solutions with discrete rotational symmetry. The cross-interaction between different spin components provides an efficient method to realize all-optical half-vortex core switching inverting its circular polarization state. This switching can be directly measured in the polarization resolved intensity in the vortex core region and it can also be applied to higher order half-vortex states.Comment: 8 pages, 8 figure

Externally Controlled Lotka-Volterra Dynamics in a Linearly Polarized Polariton Fluid

Spontaneous formation of transverse patterns is ubiquitous in nonlinear dynamical systems of all kinds. An aspect of particular interest is the active control of such patterns. In nonlinear optical systems this can be used for all-optical switching with transistor-like performance, for example realized with polaritons in a planar quantum-well semiconductor microcavity. Here we focus on a specific configuration which takes advantage of the intricate polarization dependencies in the interacting optically driven polariton system. Besides detailed numerical simulations of the coupled light-field exciton dynamics, in the present paper we focus on the derivation of a simplified population competition model giving detailed insight into the underlying mechanisms from a nonlinear dynamical systems perspective. We show that such a model takes the form of a generalized Lotka-Volterra system for two competing populations explicitly including a source term that enables external control. We present a comprehensive analysis both of the existence and stability of stationary states in the parameter space spanned by spatial anisotropy and external control strength. We also construct phase boundaries in non-trivial regions and characterize emerging bifurcations. The population competition model reproduces all key features of the switching observed in full numerical simulations of the rather complex semiconductor system and at the same time is simple enough for a fully analytical understanding of the system dynamics.Comment: 11 pages, 8 figure

(In-)Approximability Results for Interval, Resource Restricted, and Low Rank Scheduling

We consider variants of the restricted assignment problem where a set of jobs has to be assigned to a set of machines, for each job a size and a set of eligible machines is given, and the jobs may only be assigned to eligible machines with the goal of makespan minimization. For the variant with interval restrictions, where the machines can be arranged on a path such that each job is eligible on a subpath, we present the first better than 2-approximation and an improved inapproximability result. In particular, we give a (2-1/24)-approximation and show that no better than 9/8-approximation is possible, unless P=NP. Furthermore, we consider restricted assignment with R resource restrictions and rank D unrelated scheduling. In the former problem, a machine may process a job if it can meet its resource requirements regarding R (renewable) resources. In the latter, the size of a job is dependent on the machine it is assigned to and the corresponding processing time matrix has rank at most D. The problem with interval restrictions includes the 1 resource variant, is encompassed by the 2 resource variant, and regarding approximation the R resource variant is essentially a special case of the rank R+1 problem. We show that no better than 3/2, 8/7, and 3/2-approximation is possible (unless P=NP) for the 3 resource, 2 resource, and rank 3 variant, respectively. Both the approximation result for the interval case and the inapproximability result for the rank 3 variant are solutions to open challenges stated in previous works. Lastly, we also consider the reverse objective, that is, maximizing the minimal load any machine receives, and achieve similar results

Rückmeldungen aus Schulleistungstests an Lehrkräfte durch interaktive Informationsvisualisierungen

Teaching staff are expected to be able to use results from comprehensive student achieve-ment tests to improve their instruction. For these data-driven decision-making processes, skills that could be denoted as data literacy are required. Research has shown, however, that in some cases these competencies are not sufficiently pronounced and that feedback is often difficult to understand. Furthermore, the research demonstrated that it is necessary to in-crease the comprehensibility of feedback by using data visualizations. Regional state insti-tutes for education tasked with providing feedback supported teaching staff by offering fur-ther training and handouts on how to use external achievement test results. The matter of increasing the comprehensibility of feedback remains unaddressed. This gap in the research will be taken up in this thesis, which uses the example of comparative achievement tests to approach the question of whether the comprehensibility of achievement-test feedback could be increased by using a feedback system with interactive information visualizations. As part of a study with a cross-sectional design, twenty primary school teachers compared a familiar paper-based feedback for achievement-test results with a new, interactive feedback system. First, the teachers participating in the study assessed the perceived time required to answer the questions asked about the test results. Secondly, the teachers assessed how useful the feedback formats were for answering the questions. The results show that, on average, the questions asked about the data could be answered significantly more quickly using the interactive information visualizations. Furthermore, interactive information visualizations are assessed as being significantly more useful on average. Matrix visualizations were prov-en to have particularly positive effects. For the co-variables only one significant effect was perceived: Teachers with a high level of data literacy assessed the interactive feedback sys-tem as being faster. Moreover, the teachers gave statements regarding requirements for an interactive feedback system and their attitudes and experiences in working with achievement tests. The findings of this study indicate that feedback systems with a user- and demand-oriented graphic layout are becoming more important

SS-Mediziner zwischen Lagerdienst und Fronteinsatz : die personelle Besetzung der medizinischen Abteilung im Konzentrationslager Sachsenhausen 1936-1945

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Structuring co- and counter-flowing currents of polariton condensates in concentric ring-shaped potentials

We investigate the current flow of microcavity polariton condensates loaded into concentric ring-shaped potentials. The tunneling of the condensates between different potential rings results in different phase-locked states, depending on the separation of the potential rings. As a consequence, the condensate currents in different rings can flow either in the same or opposite direction depending on the specific configuration of the ring-shaped potentials. In two concentric standard ring-shaped potentials, the condensates always circulate in the same direction (co-flowing current) and the vortices formed in the two rings share the same topological charge because of the azimuthally uniform distribution of their phase difference. In this case, increasing the number of the potential rings enables the excitation of Bessel-like solutions. If the two ring-shaped potentials are engineered into an eye shape with the inner ring being standard ring-shaped and the outer ring being elliptically ring-shaped, the phase differences of the condensates in the two rings along the major and minor axes of the ellipse can be opposite, which gives rise to a counter-flowing condensate currents

Significant increase in factual knowledge with web-assisted problem-based learning as part of an undergraduate cardio-respiratory curriculum

In recent years, increasing attention has been paid to web-based learning although the advantages of computer-aided instruction over traditional teaching formats still need to be confirmed. This study examined whether participation in an online module on the differential diagnosis of dyspnoea impacts on student performance in a multiple choice examination of factual knowledge in cardiology and pneumology. A virtual problem-based learning environment for medical students supervised by postgraduate teachers was created. Seventy-four out of 183 fourth-year medical students volunteered to use the online module while attending a 6-week cardio-respiratory curriculum in summer 2007. Of these, 40 were randomly selected to be included (intervention group); the remaining 34 served as an internal control group. Analysis of all written exams taken during the preceding term showed that both groups were comparable (86.4 ± 1.1 vs. 85.9 ± 1.1%; p = 0.751). Students in the intervention group scored significantly higher in the final course assessment than students allocated to the control group (84.8 ± 1.3 vs. 79.5 ± 1.4%; p = 0.006; effect size 0.67). Thus, additional problem-based learning with an online module as part of an undergraduate cardio-respiratory curriculum lead to higher students’ scores in an exam testing factual knowledge. Whether using this teaching format increases overall student motivation to engage in the learning process needs to be further investigated

Scheduling with Many Shared Resources

Consider the many shared resource scheduling problem where jobs have to be scheduled on identical parallel machines with the goal of minimizing the makespan. However, each job needs exactly one additional shared resource in order to be executed and hence prevents the execution of jobs that need the same resource while being processed. Previously a $(2m/(m+1))$-approximation was the best known result for this problem. Furthermore, a $6/5$-approximation for the case with only two machines was known as well as a PTAS for the case with a constant number of machines. We present a simple and fast 5/3-approximation and a much more involved but still reasonable 1.5-approximation. Furthermore, we provide a PTAS for the case with only a constant number of machines, which is arguably simpler and faster than the previously known one, as well as a PTAS with resource augmentation for the general case. The approximation schemes make use of the N-fold integer programming machinery, which has found more and more applications in the field of scheduling recently. It is plausible that the latter results can be improved and extended to more general cases. Lastly, we give a $5/4 - \varepsilon$ inapproximability result for the natural problem extension where each job may need up to a constant number (in particular $3$) of different resources