Time-frequency analysis on the adeles over the rationals

We show that the construction of Gabor frames in $L^{2}(\mathbb{R})$ with generators in $\mathbf{S}_{0}(\mathbb{R})$ and with respect to time-frequency shifts from a rectangular lattice $\alpha\mathbb{Z}\times\beta\mathbb{Z}$ is equivalent to the construction of certain Gabor frames for $L^{2}$ over the adeles over the rationals and the group $\mathbb{R}\times\mathbb{Q}_{p}$. Furthermore, we detail the connection between the construction of Gabor frames on the adeles and on $\mathbb{R}\times\mathbb{Q}_{p}$ with the construction of certain Heisenberg modules.Comment: minor revisions, added more references, added a Balian-Low type result in the form of Proposition 4.

Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

High-bandwidth transfer of phase stability through a fiber frequency comb

We demonstrate phase locking of a 729 nm diode laser to a 1542 nm master laser via an erbium-doped-fiber frequency comb, using a transfer-oscillator feedforward scheme which suppresses the effect of comb noise in an unprecedented 1.8 MHz bandwidth. We illustrate its performance by carrying out coherent manipulations of a trapped calcium ion with 99 % fidelity even at few-microsecond timescales. We thus demonstrate that transfer-oscillator locking can provide sufficient phase stability for high-fidelity quantum logic manipulation even without pre-stabilization of the slave diode laser.Comment: 6 pages, 3 figures. To be published in Optics Express. Clarified method for measuring laser noise spectra. Improved spectroscopic data in Fig. 3, with motional decoherence now suppresse

Estimating the density scaling exponent of viscous liquids from specific heat and bulk modulus data

It was recently shown by computer simulations that a large class of liquids exhibits strong correlations in their thermal fluctuations of virial and potential energy [Pedersen et al., Phys. Rev. Lett. 100, 015701 (2008)]. Among organic liquids the class of strongly correlating liquids includes van der Waals liquids, but excludes ionic and hydrogen-bonding liquids. The present note focuses on the density scaling of strongly correlating liquids, i.e., the fact their relaxation time tau at different densities rho and temperatures T collapses to a master curve according to the expression tau propto F(rho^gamma/T) [Schroder et al., arXiv:0803.2199]. We here show how to calculate the exponent gamma from bulk modulus and specific heat data, either measured as functions of frequency in the metastable liquid or extrapolated from the glass and liquid phases to a common temperature (close to the glass transition temperature). Thus an exponent defined from the response to highly nonlinear parameter changes may be determined from linear response measurements

Politiets forebyggende innsats i skolen : en teoretisk oppgave

Bachelor i politiutdannin

Semiconductor resonator solitons above band gap

We show experimentally the existence of bright and dark spatial solitons in semiconductor resonators for excitation above the band gap energy. These solitons can be switched on, both spontaneously and with address pulses, without the thermal delay found for solitons below the band gap which is unfavorable for applications. The differences between soliton properties above and below gap energy are discussed.Comment: 4 pages, 7 figure

Supercooled Liquid Dynamics Studied via Shear-Mechanical Spectroscopy

We report dynamical shear-modulus measurements for five glass-forming liquids (pentaphenyl trimethyl trisiloxane, diethyl phthalate, dibutyl phthalate, 1,2-propanediol, and m-touluidine). The shear-mechanical spectra are obtained by the piezoelectric shear-modulus gauge (PSG) method. This technique allows one to measure the shear modulus ($10^{5} -10^{10}$ Pa) of the liquid within a frequency range from 1 mHz to 10 kHz. We analyze the frequency-dependent response functions to investigate whether time-temperature superposition (TTS) is obeyed. We also study the shear-modulus loss-peak position and its high-frequency part. It has been suggested that when TTS applies, the high-frequency side of the imaginary part of the dielectric response decreases like a power law of the frequency with an exponent -1/2. This conjecture is analyzed on the basis of the shear mechanical data. We find that TTS is obeyed for pentaphenyl trimethyl trisiloxane and in 1,2-propanediol while in the remaining liquids evidence of a mechanical $\beta$ process is found. Although the the high-frequency power law behavior $\omega^{-\alpha}$ of the shear-loss may approach a limiting value of $\alpha=0.5$ when lowering the temperature, we find that the exponent lies systematically above this value (around 0.4). For the two liquids without beta relaxation (pentaphenyl trimethyl trisiloxane and 1,2-propanediol) we also test the shoving model prediction, according to which the the relaxation-time activation energy is proportional to the instantaneous shear modulus. We find that the data are well described by this model.Comment: 7 pages, 6 figure

Analysis of the Effects of Five Factors Relevant to In Vitro Chondrogenesis of Human Mesenchymal Stem Cells Using Factorial Design and High Throughput mRNA-Profiling

The in vitro process of chondrogenic differentiation of mesenchymal stem cells for tissue engineering has been shown to require three-dimensional culture along with the addition of differentiation factors to the culture medium. In general, this leads to a phenotype lacking some of the cardinal features of native articular chondrocytes and their extracellular matrix. The factors used vary, but regularly include members of the transforming growth factor β superfamily and dexamethasone, sometimes in conjunction with fibroblast growth factor 2 and insulin-like growth factor 1, however the use of soluble factors to induce chondrogenesis has largely been studied on a single factor basis. In the present study we combined a factorial quality-by-design experiment with high-throughput mRNA profiling of a customized chondrogenesis related gene set as a tool to study in vitro chondrogenesis of human bone marrow derived mesenchymal stem cells in alginate. 48 different conditions of transforming growth factor β 1, 2 and 3, bone morphogenetic protein 2, 4 and 6, dexamethasone, insulin-like growth factor 1, fibroblast growth factor 2 and cell seeding density were included in the experiment. The analysis revealed that the best of the tested differentiation cocktails included transforming growth factor β 1 and dexamethasone. Dexamethasone acted in synergy with transforming growth factor β 1 by increasing many chondrogenic markers while directly downregulating expression of the pro-osteogenic gene osteocalcin. However, all factors beneficial to the expression of desirable hyaline cartilage markers also induced undesirable molecules, indicating that perfect chondrogenic differentiation is not achievable with the current differentiation protocols