An uncertainty principle for the Dunkl transform - Rösler, Margit (Bulletin of the Australian Mathematical Society)
This note presents an analogue of the classical Heisenberg-Weyl uncertainty principle for the Dunkl transform on ℝ N . Its proof is based on expansions with respect to generalised Hermite functions.
Keywords: General Mathematics

Positivity of Dunkl’s intertwining operator - Rösler, Margit (Duke Mathematical Journal)
Keywords: General Mathematics

Partial Characters and Signed Quotient Hypergroups - Rösler, Margit; Voit, Michael (Canadian Journal of Mathematics)
Abstract If G is a closed subgroup of a commutative hypergroup K , then the coset space K / G carries a quotient hypergroup structure. In this paper, we study related convolution structures on K / G coming fromdeformations of the quotient hypergroup structure by certain functions on K which we call partial characters with respect to G . They are usually not probability-preserving, but lead to so-called signed hypergroups on K / G . A first example is provided by the Laguerre convolution on [0, ∞[, which is interpreted as a signed quotient hypergroup convolution derived from the Heisenberg group. Moreover, signed hypergroups associated with the Gelfand pair ( U ( n , 1), U ( n )) are discussed.
Keywords: General Mathematics

On Polynomial Decompositions - Klüners, Jürgen (Journal of Symbolic Computation)
We present a new polynomial decomposition which generalizes the functional and homogeneous bivariate decomposition of irreducible monic polynomials in one variable over the rationals. With these decompositions it is possible to calculate the roots of an imprimitive polynomial by solving polynomial equations of lower degree.
Keywords: Computational Mathematics; Algebra and Number Theory

Computing Automorphisms of Abelian Number Fields - Klüners, Jürgen; Acciaro, Vincenzo (Mathematics of Computation)
Let L = ℚ(α) be an abelian number field of degree n. Most algorithms for computing the lattice of subfields of L require the computation of all the conjugates of α. This is usually achieved by factoring the minimal polynomial mα(x) of α over L. In practice, the existing algorithms for factoring polynomials over algebraic number fields can handle only problems of moderate size. In this paper we describe a fast probabilistic algorithm for computing the conjugates of α, which is based on p-adic techniques. Given mα(x) and a rational prime p which does not divide the discriminant disc(mα(x)) of mα(x), the algorithm computes the Frobenius automorphism of p in time polynomial in the size of p and in the size of mα(x). By repeatedly applying the algorithm to randomly chosen primes it is possible to compute all the conjugates of α.

Multiple K-edge XAS for the structural analysis of thiophenolate bridged heterotrinuclear complexes - Meyer-Klaucke, W.; Glaser, T.; Fröba, M.; Tiemann, Michael; Wong, J.; Trautwein, A. X. (Journal of Synchrotron Radiation)
Multiple K-edge XAS for the structural analysis of thiophenolate bridged heterotrinuclear complexes

Influence of carrier correlations on the excitonic optical response including disorder and microcavity effects - Meier, Torsten; Sieh, C.; Knorr, A.; Jahnke, F.; Thomas, P.; Koch, S.W. (The European Physical Journal B-Condensed Matter and Complex Systems)
A model study of the characteristic signatures of carrier-correlation effects on the excitonic differential absorption spectra in semiconductors is presented. Using an effectively one-dimensional tight-binding system Coulomb-induced carrier-correlations up to third-order in the optical field are treated without additional approximations. To illustrate the influence of the different many-body contributions excitonic differential absorption spectra are computed for various polarizations and pump-probe time delays. The simultaneous influence of energetic disorder and correlations on the differential absorption spectra is discussed. Also presented are numerical results for the case when the semiconductor system is placed inside a microcavity in the strong-coupling regime. It is shown that the correlations induce characteristic signatures in the normal mode spectra.

Theory of coherent effects in semiconductors - Meier, Torsten; Koch, S.W.; Sieh, C.; Jahnke, F.; Knorr, A.; Brick, P.; Hübner, M.; Ell, C.; Prineas, J.; Khitrova , G.; Gibbs, H.M. (Journal of luminescence)
A microscopic theory is applied to discuss coherent excitation effects in semiconductors. The theory is evaluated to analyze ultrafast absorption changes around the exciton resonance in semiconductor quantum-well structures where the relative strength of the different many-body contributions can be manipulated by proper selection of pump and probe polarizations. For two-band systems and oppositely circular polarization it is shown that Coulombic correlation dynamics dominates the optical response. As a consequence, the optical Stark effect in this configuration corresponds to a red shift of the exciton resonance in striking contrast to the usual atomic-like blue shift. The predictions are confirmed by experiments using high-quality InGaAs quantum-well systems.

Scaling Of Fluorescence Stokes Shift And Superradiance Coherence Size In Disordered Molecular Aggregates - Meier, Torsten (The Journal of Physical Chemistry A)
Fluorescence line shapes and cooperative spontaneous emission in disordered one-dimensional molecular aggregates are calculated using closed expressions derived by applying the method of optimal fluctuation. A simple scaling relation Ls ∼ ωs-1/2 is established between the low temperature disorder-induced Stokes shift ωs and the superradiance enhancement factor Ls. Scaling of the Stokes shift with aggregate size, and the time-dependent Stokes shift are discussed as well. Excellent agreement is obtained with numerical simulations.

Informations- und Kommunikationstechnologien im Kontext der kontrollgesellschaftlichen Umstrukturierung (Information- and communication-technologies in the context of the transformation towards a society of control). October 1998 - Fuchs, Christian (Talk at the 20th Congress Political Psychology “Sozialisation und Identitäten. Politische Kultur im Umbruch?“, Hamburg, 15.-18. In Moser, Helmut, ed. 1999 Sozialisation und Identitäten - Politische Kultur im Umbruch)

Synthesis and Al K-Edge Xanes Investigation of Mesostructured Aluminophosphates - Tiemann, Michael; Fröba, M.; Wong, J. (MRS Proceedings)
We report on the synthesis of lamellar mesostructured aluminophosphate composites which contain variable relative amounts of aluminium oxide species in the core regions of the lamellae; this is investigated quantitatively by Al K-edge XANES spectroscopy. Templating is achieved by the utilisation of monododecyl phosphate surfactant. If no phosphorous source (such as H3PO4) is used for the synthesis, the phosphate head groups of the surfactant become incorporated into the inorganic network to form similar lamellar aluminophosphate structures. Thus, the surfactant serves as both template and reactant.

High rate CVD-diamond etching for high temperature pressure sensor applications - Otterbach, R.; Hilleringmann, Ulrich (29th European Solid-State Device Research Conference)

Intraband terahertz emission from coupled semiconductor quantum wells: A model study using the exciton representation - Meier, Torsten; Zhang, W.M.; Chernyak, V.; Mukamel, S. (Physical Review B)
Intraband emission resulting from the second-order polarization induced by a femtosecond pump field in semiconductor nanostructures is calculated. The two-band model is transformed to the exciton representation, and exciton-phonon coupling represented by arbitrary spectral densities is incorporated into the equations of motion for the relevant exciton variables through Redfield superoperators. Time-resolved coherent and incoherent terahertz radiation as well as the incoherent optical fluorescence are calculated for a one-dimensional model of coupled quantum wells in an external electric field with on-site Coulomb interaction between electrons and holes and an overdamped Brownian oscillator spectral density representing the electron-phonon coupling. A doorway-window picture based on the reduced single-electron density matrix is developed for the analysis of both signals. Disorder and phonon-induced dephasing effects on the various signals are discussed and compared.

From exciton resonance to frequency mixing in GaAs multiple quantum wells - Meier, Torsten; Ahn, Y. H.; Yahng, J. S.; Sohn, J. Y.; Yee, K. J.; Hohng, S. C.; Woo, J. C.; Kim, D. S.; Koch, S.W.; Lim, Y. S.; Kim, E. K. (Physical review letters)
Frequency mixing ( 2ω1−ω2) is demonstrated in femtosecond nondegenerate four-wave mixing (FWM) on GaAs multiple quantum wells using two synchronized, independently tunable lasers. The frequency mixing component in the spectrally resolved FWM coexists with the exciton resonance, and it dominates over the exciton component at high intensity and high detuning. This off-resonant component is present only for delays smaller than the temporal pulse width, whereas the resonant exciton component survives for longer delays.

Coulomb memory signatures in the excitonic optical Stark effect - Meier, Torsten; Sieh, C.; Jahnke, F.; Knorr, A.; Koch, S.W.; Brick, P.; Hübner, M.; Ell, C.; Prineas, J.; Khitrova, G.; Gibbs, H.M. (Physical review letters)
Differential absorption spectra of high-quality InGaAs quantum wells are presented for various pump detunings and polarization configurations. For low intensity pump pulses tuned well below the exciton a redshift is observed for opposite circularly polarized probe pulses. Microscopic calculations show that this redshift originates from memory effects in the Coulomb-induced excitonic correlations.

Coherent excitation spectroscopy on inhomogeneous exciton ensembles - Meier, Torsten; Euteneuer, A.; Finger, E.; Hofmann, M.; Stolz, W.; Thomas, P.; Koch, S.W.; Rühle, W.W.; Hey, R.; Ploog, K. (Physical review letters)
A new spectroscopic technique is demonstrated on three characteristically different semiconductor quantum-well samples. Coherent excitation spectroscopy reveals coherent coupling and effectively suppresses the signatures of inhomogeneous broadening and incoherent transfer between various excitonic states in quantum wells. Coherently coupled homogeneous subsystems are analyzed in an inhomogeneously broadened excitonic ensemble.

Superradiance Coherence Sizes in Single-Molecule Spektroscopy of LH2 Antenna Complexes - Meier, Torsten; Zhao, Y.; Zhang, W.M.; Chernyak, V.; Mukamel, S. (The Journal of Physical Chemistry B)
The distribution of cooperative radiative decay rates in photosynthetic aggregates is calculated using a Frenkel exciton model with static diagonal disorder. This distribution which depends on both the exciton coherence sizes and the aggregate geometry can be directly observed using single-molecule spectroscopy. Comparison is made with a dynamic exciton self-trapping (polaron) mechanism for localization.

Excitons versus unbound electron-hole pairs and their influence on exciton bleaching: A model study - Meier, Torsten; Koch, S.W. (Physical Review B)
Absorption changes in semiconductors induced by low-density populations are calculated using a one-dimensional model. The microscopic analysis includes Coulomb-induced many-body correlations and reveals distinct signatures of six particle correlations. The strength of exciton bleaching induced by excitons and electron-hole pairs is compared and analyzed.

Femtosecond four-wave-mixing spectroscopy of interacting magnetoexcitons in semiconductor quantum wells - Meier, Torsten; Yokojima, S.; Chernyak, V.; Mukamel, S. (Physical Review B)
Nonlinear exciton equations for one- and two-exciton variables, obtained by mapping the two-band model onto the molecular (Frenkel) Hamiltonian, are applied to calculate resonant optical nonlinearities in two-dimensional semiconductors in a strong perpendicular magnetic field. The polarization dependence of the time-resolved four-wave-mixing signals provides a direct probe for the two-exciton manifold as well as for the asymmetry of the particle-particle and particle-hole Coulomb interactions.

Helmut Klotz: Der Pfaffe und der Alchimist. Was Chemiker von Theologen wissen sollten und umgekehrt, Stuttgart 1999 - Schroeter-Wittke, Harald (http://www.amazon.de)