Optical absorption in quantum dots: Coupling to longitudinal optical phonons treated exactly

Optical transitions in a semiconductor quantum dot are theoretically investigated, with emphasis on the coupling to longitudinal optical phonons, and including excitonic effects. When limiting to a finite number of $m$ electron and $n$ hole levels in the dot, the model can be solved exactly within numerical accuracy. Crucial for this to work is the absence of dispersion of the phonons. A suitable orthogonalization procedure leaves only $m(m+1)/2+n(n+1)/2-2$ phonon modes to be coupled to the electronic system. We calculate the linear optical polarization following a delta pulse excitation, and by a subsequent Fourier transformation the resulting optical absorption. This strict result is compared with a frequently used approximation modeling the absorption as a convolution between spectral functions of electron and hole, which tends to overestimate the effect of the phonon coupling. Numerical results are given for two electron and three hole states in a quantum dot made from the polar material CdSe. Parameter values are chosen such that a quantum dot with a resonant sublevel distance can be compared with a nonresonant one.Comment: 12 pages, 6 figure

Estimating regional unemployment with mobile network data for Functional Urban Areas in Germany

The ongoing growth of cities due to better job opportunities is leading to increased labour-relatedcommuter flows in several countries. On the one hand, an increasing number of people commuteand move to the cities, but on the other hand, the labour market indicates higher unemployment ratesin urban areas than in the surrounding areas. We investigate this phenomenon on regional level byan alternative definition of unemployment rates in which commuting behaviour is integrated. Wecombine data from the Labour Force Survey (LFS) with dynamic mobile network data by small areamodels for the federal state North Rhine-Westphalia in Germany. From a methodical perspective, weuse a transformed Fay-Herriot model with bias correction for the estimation of unemployment ratesand propose a parametric bootstrap for the Mean Squared Error (MSE) estimation that includes thebias correction. The performance of the proposed methodology is evaluated in a case study based onofficial data and in model-based simulations. The results in the application show that unemploymentrates (adjusted by commuters) in German cities are lower than traditional official unemployment ratesindicate

Random Lasing in an Inhomogeneous and Disordered System of Cold Atoms

We consider light trapping in an amplifying medium consisting of cold alkali-metal atoms; the atomic gas plays a dual role as a scattering and as a gain medium. We perform Monte-Carlo simulations for the combined processes. In some configurations of the inhomogeneous distribution this leads to a point of instability behavior and a signature of random lasing in a cold atomic gas.Comment: 10 pages, 5 figure

Light scattering and dissipative dynamics of many fermionic atoms in an optical lattice

We investigate the many-body dissipative dynamics of fermionic atoms in an optical lattice in the presence of incoherent light scattering. Deriving and solving a master equation to describe this process microscopically for many particles, we observe contrasting behaviour in terms of the robustness against this type of heating for different many-body states. In particular, we find that the magnetic correlations exhibited by a two-component gas in the Mott insulating phase should be particularly robust against decoherence from light scattering, because the decoherence in the lowest band is suppressed by a larger factor than the timescales for effective superexchange interactions that drive coherent dynamics. Furthermore, the derived formalism naturally generalizes to analogous states with SU(N) symmetry. In contrast, for typical atomic and laser parameters, two-particle correlation functions describing bound dimers for strong attractive interactions exhibit superradiant effects due to the indistinguishability of off-resonant photons scattered by atoms in different internal states. This leads to rapid decay of correlations describing off-diagonal long-range order for these states. Our predictions should be directly measurable in ongoing experiments, providing a basis for characterising and controlling heating processes in quantum simulation with fermions.Comment: 18 pages, 7 figure

Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle

We present a detailed analysis of the 1D expansion of a coherent interacting matterwave (a Bose-Einstein condensate) in the presence of disorder. A 1D random potential is created via laser speckle patterns. It is carefully calibrated and the self-averaging properties of our experimental system are discussed. We observe the suppression of the transport of the BEC in the random potential. We discuss the scenario of disorder-induced trapping taking into account the radial extension in our experimental 3D BEC and we compare our experimental results with the theoretical predictions

Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web

We study the topology of the Megaparsec Cosmic Web in terms of the scale-dependent Betti numbers, which formalize the topological information content of the cosmic mass distribution. While the Betti numbers do not fully quantify topology, they extend the information beyond conventional cosmological studies of topology in terms of genus and Euler characteristic. The richer information content of Betti numbers goes along the availability of fast algorithms to compute them. For continuous density fields, we determine the scale-dependence of Betti numbers by invoking the cosmologically familiar filtration of sublevel or superlevel sets defined by density thresholds. For the discrete galaxy distribution, however, the analysis is based on the alpha shapes of the particles. These simplicial complexes constitute an ordered sequence of nested subsets of the Delaunay tessellation, a filtration defined by the scale parameter, $\alpha$. As they are homotopy equivalent to the sublevel sets of the distance field, they are an excellent tool for assessing the topological structure of a discrete point distribution. In order to develop an intuitive understanding for the behavior of Betti numbers as a function of $\alpha$, and their relation to the morphological patterns in the Cosmic Web, we first study them within the context of simple heuristic Voronoi clustering models. Subsequently, we address the topology of structures emerging in the standard LCDM scenario and in cosmological scenarios with alternative dark energy content. The evolution and scale-dependence of the Betti numbers is shown to reflect the hierarchical evolution of the Cosmic Web and yields a promising measure of cosmological parameters. We also discuss the expected Betti numbers as a function of the density threshold for superlevel sets of a Gaussian random field.Comment: 42 pages, 14 figure