Decay rate of a Wannier exciton in low dimensional systems

The superradiant decay rate of Wannier exciton in one dimensional system is studied. The crossover behavior from 1D chain to 2D film is also examined. It is found that the decay rate shows oscillatory dependence on channel width L. When the quasi 1-D channel is embeded with planar microcavities, it is shown that the dark mode exciton can be examined experimentally.Comment: 12 pages, 1 figur

Semantics-Space-Time Cube. A Conceptual Framework for Systematic Analysis of Texts in Space and Time

We propose an approach to analyzing data in which texts are associated with spatial and temporal references with the aim to understand how the text semantics vary over space and time. To represent the semantics, we apply probabilistic topic modeling. After extracting a set of topics and representing the texts by vectors of topic weights, we aggregate the data into a data cube with the dimensions corresponding to the set of topics, the set of spatial locations (e.g., regions), and the time divided into suitable intervals according to the scale of the planned analysis. Each cube cell corresponds to a combination (topic, location, time interval) and contains aggregate measures characterizing the subset of the texts concerning this topic and having the spatial and temporal references within these location and interval. Based on this structure, we systematically describe the space of analysis tasks on exploring the interrelationships among the three heterogeneous information facets, semantics, space, and time. We introduce the operations of projecting and slicing the cube, which are used to decompose complex tasks into simpler subtasks. We then present a design of a visual analytics system intended to support these subtasks. To reduce the complexity of the user interface, we apply the principles of structural, visual, and operational uniformity while respecting the specific properties of each facet. The aggregated data are represented in three parallel views corresponding to the three facets and providing different complementary perspectives on the data. The views have similar look-and-feel to the extent allowed by the facet specifics. Uniform interactive operations applicable to any view support establishing links between the facets. The uniformity principle is also applied in supporting the projecting and slicing operations on the data cube. We evaluate the feasibility and utility of the approach by applying it in two analysis scenarios using geolocated social media data for studying people's reactions to social and natural events of different spatial and temporal scales

The K\"ahler Potential of Abelian Higgs Vortices

We calculate the K\"ahler potential for the Samols metric on the moduli space of Abelian Higgs vortices on \mathbbm{R}^{2}, in two different ways. The first uses a scaling argument. The second is related to the Polyakov conjecture in Liouville field theory. The K\"ahler potential on the moduli space of vortices on \mathbbm{H}^{2} is also derived, and we are led to a geometrical reinterpretation of these vortices. Finally, we attempt to find the K\"ahler potential for vortices on \mathbbm{R}^{2} in a third way by relating the vortices to SU(2) Yang-Mills instantons on \mathbbm{R}^{2}\times S^{2}. This approach does not give the correct result, and we offer a possible explanation for this.Comment: 25 page