On the number of conjugacy classes of maximal subgroups in a finite soluble group

We show that for many formations U-fraktur sign, there exists an integer n = m̄(U-fraktur sign) such that every finite soluble group G not belonging to the class U-fraktur sign has at most n conjugacy classes of maximal subgroups belonging to the class U-fraktur sign. If U-fraktur sign is a local formation with formation function f, we bound m̄(U-fraktur sign) in terms of the m̄(f(p)) (p ∈ ℙ). In particular, we show that m̄(ℜk) = k + 1 for every nonnegative integer k, where ℜk is the class of all finite groups of Fitting length ≦ k

Modally Resolved Fabry-Perot Experiment with Semiconductor Waveguides

Based on the interaction between different spatial modes, semiconductor Bragg-reflection waveguides provide a highly functional platform for non-linear optics. Therefore, the control and engineering of the properties of each spatial mode is essential. Despite the multimodeness of our waveguide, the well-established Fabry-Perot technique for recording fringes in the optical transmission spectrum can successfully be employed for a detailed linear optical characterization when combined with Fourier analysis. A prerequisite for the modal sensitivity is a finely resolved transmission spectrum that is recorded over a broad frequency band. Our results highlight how the features of different spatial modes, such as their loss characteristics and dispersion properties, can be separated from each other allowing their comparison. The mode-resolved measurements are important for optimizing the performance of such multimode waveguides by tailoring the properties of their spatial modes.Comment: 8 pages, 7 figure

Multi-dimensional laser spectroscopy of exciton-polaritons with spatial light modulators

We describe an experimental system that allows one to easily access the dispersion curve of exciton-polaritons in a microcavity. Our approach is based on two spatial light modulators (SLM), one for changing the excitation angles (momenta), and the other for tuning the excitation wavelength. We show that with this setup, an arbitrary number of states can be excited accurately and that re-configuration of the excitation scheme can be done at high speed.Comment: 4 pages, 5 figure

Open Systems out of Equilibrium: Theory and Simulation

We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution molecular dynamics technique (AdResS). We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with results obtained from the simulation of a larger, locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.Comment: page 1-6 main manuscript with 3 figures, page 7-11 supplementary material with 4 figure

The Localization Transition of the Two-Dimensional Lorentz Model

We investigate the dynamics of a single tracer particle performing Brownian motion in a two-dimensional course of randomly distributed hard obstacles. At a certain critical obstacle density, the motion of the tracer becomes anomalous over many decades in time, which is rationalized in terms of an underlying percolation transition of the void space. In the vicinity of this critical density the dynamics follows the anomalous one up to a crossover time scale where the motion becomes either diffusive or localized. We analyze the scaling behavior of the time-dependent diffusion coefficient D(t) including corrections to scaling. Away from the critical density, D(t) exhibits universal hydrodynamic long-time tails both in the diffusive as well as in the localized phase.Comment: 13 pages, 7 figures

Uncovering dispersion properties in semiconductor waveguides to study photon-pair generation

This work was supported by the FWF through project no. I-2065-N27, the DFG Project no. SCHN1376/2-1, the ERC project EnSeNa (257531) and the State of Bavaria.We investigate the dispersion properties of ridge Bragg-reflection waveguides to deduce their phasematching characteristics. These are crucial for exploiting them as sources of parametric down-conversion (PDC). In order to estimate the phasematching bandwidth we first determine the group refractive indices of the interacting modes via Fabry–Perot experiments in two distant wavelength regions. Second, by measuring the spectra of the emitted PDC photons, we gain access to their group index dispersion. Our results offer a simple approach for determining the PDC process parameters in the spectral domain, and provide important feedback for designing such sources, especially in the broadband case.Publisher PDFPeer reviewe

Long-Time Behavior of Velocity Autocorrelation Function for Interacting Particles in a Two-Dimensional Disordered System

The long-time behavior of the velocity autocorrelation function (VACF) is investigated by the molecular dynamics simulation of a two-dimensional system which has both a many-body interaction and a random potential. With strengthening the random potential by increasing the density of impurities, a crossover behavior of the VACF is observed from a positive tail, which is proportional to t^{-1}, to a negative tail, proportional to -t^{-2}. The latter tail exists even when the density of particles is the same order as the density of impurities. The behavior of the VACF in a nonequilibrium steady state is also studied. In the linear response regime the behavior is similar to that in the equilibrium state, whereas it changes drastically in the nonlinear response regime.Comment: 12 pages, 5 figure