Time domain beam propagation method for the simulation of temporal solitons in periodic media

A time domain beam propagation method for the simulation of optical pulses propagating through Kerr-nonlinear structures is presented. The method is verified by simulation of the known solitary wave solutions in nonlinear periodic medi

Photochemistry of Coordination Compounds of the Main Group Metals

A general concept is developed which relates characteristics excited states of main group metal complexes to typical photoreactions. With regard to their electronic spectra and photochemistry the main group metals are classified according to their ground state electron configuration nsxnpy. The photochemistry is generally dominated by the reactivity of metal-centered sp and ligand to metal charge transfer excited states which in most cases initiate inter- and intramolecular photoredox processes

SGR J1550–5418 Bursts Detected with the Fermi Gamma-Ray Burst Monitor during its Most Prolific Activity

We have performed detailed temporal and time-integrated spectral analysis of 286 bursts from SGR J1550–5418 detected with the Fermi Gamma-ray Burst Monitor (GBM) in 2009 January, resulting in the largest uniform sample of temporal and spectral properties of SGR J1550–5418 bursts. We have used the combination of broadband and high time-resolution data provided with GBM to perform statistical studies for the source properties. We determine the durations, emission times, duty cycles, and rise times for all bursts, and find that they are typical of SGR bursts. We explore various models in our spectral analysis, and conclude that the spectra of SGR J1550–5418 bursts in the 8-200 keV band are equally well described by optically thin thermal bremsstrahlung (OTTB), a power law (PL) with an exponential cutoff (Comptonized model), and two blackbody (BB) functions (BB+BB). In the spectral fits with the Comptonized model, we find a mean PL index of –0.92, close to the OTTB index of –1. We show that there is an anti-correlation between the Comptonized E_(peak) and the burst fluence and average flux. For the BB+BB fits, we find that the fluences and emission areas of the two BB functions are correlated. The low-temperature BB has an emission area comparable to the neutron star surface area, independent of the temperature, while the high-temperature BB has a much smaller area and shows an anti-correlation between emission area and temperature. We compare the properties of these bursts with bursts observed from other SGR sources during extreme activations, and discuss the implications of our results in the context of magnetar burst models

A Stark decelerator on a chip

A microstructured array of 1254 electrodes on a substrate has been configured to generate an array of local minima of electric field strength with a periodicity of 120 $\mu$m about 25 $\mu$m above the substrate. By applying sinusoidally varying potentials to the electrodes, these minima can be made to move smoothly along the array. Polar molecules in low-field seeking quantum states can be trapped in these traveling potential wells. Recently, we experimentally demonstrated this by transporting metastable CO molecules at constant velocities above the substrate [Phys. Rev. Lett. 100 (2008) 153003]. Here, we outline and experimentally demonstrate how this microstructured array can be used to decelerate polar molecules directly from a molecular beam. For this, the sinusoidally varying potentials need to be switched on when the molecules arrive above the chip, their frequency needs to be chirped down in time, and they need to be switched off before the molecules leave the chip again. Deceleration of metastable CO molecules from an initial velocity of 360 m/s to a final velocity as low as 240 m/s is demonstrated in the 15-35 mK deep potential wells above the 5 cm long array of electrodes. This corresponds to a deceleration of almost $10^5$ $g$, and about 85 cm$^{-1}$ of kinetic energy is removed from the metastable CO molecules in this process.Comment: 17 pages, 6 figure

State space formulas for stable rational matrix solutions of a Leech problem

Given stable rational matrix functions $G$ and $K$, a procedure is presented to compute a stable rational matrix solution $X$ to the Leech problem associated with $G$ and $K$, that is, $G(z)X(z)=K(z)$ and $\sup_{|z|\leq 1}\|X(z)\|\leq 1$. The solution is given in the form of a state space realization, where the matrices involved in this realization are computed from state space realizations of the data functions $G$ and $K$.Comment: 25 page

All solutions to the relaxed commutant lifting problem

A new description is given of all solutions to the relaxed commutant lifting problem. The method of proof is also different from earlier ones, and uses only an operator-valued version of a classical lemma on harmonic majorants.Comment: 15 page

State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution

For the strictly positive case (the suboptimal case) the maximum entropy solution $X$ to the Leech problem $G(z)X(z)=K(z)$ and $\|X\|_\infty=\sup_{|z|\leq 1}\|X(z)\|\leq 1$, with $G$ and $K$ stable rational matrix functions, is proved to be a stable rational matrix function. An explicit state space realization for $X$ is given, and $\|X\|_\infty$ turns out to be strictly less than one. The matrices involved in this realization are computed from the matrices appearing in a state space realization of the data functions $G$ and $K$. A formula for the entropy of $X$ is also given.Comment: 19 page