On excitation transfer and relaxation models in low-temperature systems

Starting from Redfield's reduced density formalism, we derive the coupled relaxation equations and expressions for the rate constants applicable to excited dimer systems In a comparative discussion the limitations are shown of relaxation models derived previously.     

The combinatorics of the bar resolution in group cohomology

We study a combinatorially defined double complex structure on the ordered chains of any simplicial complex. Its columns are related to the cell complex K_n whose face poset is isomorphic to the subword ordering on words without repetition from an alphabet of size n. This complex is shellable and as an application we give a representation theoretic interpretation for derangement numbers and a related symmetric function considered by Désarménien and Wachs [11].

We analyze the two spectral sequences arising from the double complex in the case of the bar resolution for a group. This spectral sequence converges to the cohomology of the group and provides a method for computing group cohomology in terms of the cohomology of subgroups. Its behavior is influenced by the complex of oriented chains of the simplicial complex of finite subsets of the group, and we examine the Ext class of this complex.     

A quasiconformal dynamic property of the disk

It is known that every conformai embedding of the disk into the extended complex plane possesses a r²-quasiconformal extension across eachr-level line (the r²-property of a domain). We show here that this is a characteristic property of the disk: any simply connected domain which is not a disk does not admit ther ²-property. Supported by the RiP-program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach.     

Weyl Group $${varvec{q}}$$ q -Kreweras Numbers and Cyclic Sieving

Catalan numbers are known to count noncrossing set partitions, while Narayana and Kreweras numbers refine this count according to the number of blocks in the set partition, and by its collection of block sizes. Motivated by reflection group generalizations of Catalan numbers and their q-analogues, this paper concerns a definition of q-Kreweras numbers for finite Weyl groups W, refining the q-Catalan numbers for W, and arising from work of the second author. We give explicit formulas in all types for the q-Kreweras numbers. In the classical types A, B, C, we also record formulas for the q-Narayana numbers and in the process show that the formulas depend only on the Weyl group (that is, they coincide in types B and C). In addition, we verify that in the classical types A, B, C, D the q-Kreweras numbers obey the expected cyclic sieving phenomena when evaluated at appropriate roots of unity.

     

Heteroclinic cycles for reaction diffusion systems by forced symmetry-breaking

Recently it has been observed, that perturbations of symmetric ODE's can lead to highly nontrivial dynamics. In this paper we want to establish a similar result for certain nonlinear partial differential systems. Our results are applied to equations which are motivated from chemical reactions. In fact we show that the theory applies to the Brusselator on a sphere. To be more precise, we consider solutions of a semi-linear parabolic equation on the 2-sphere. When this equation has an axisymmetric equilibrium , the group orbit of (under rotations) gives a whole (invariant) manifold of equilibria. Under generic conditions we have that, after perturbing our equation by a (small) -equivariant perturbation, persists as an invariant manifold . However, the flow on is in general no longer trivial. Indeed, we find slow dynamics on and, in the case (the tetrahedral subgroup of ), we observe heteroclinic cycles. In the application to chemical systems we would expect intermittent behaviour. However, for the Brusselator equations this phenomenon is not stable. In order to see it in a physically relevant situation we need to introduce further terms to get a higher codimension bifurcation.

     

Capture and release of a conditional state of a cavity QED system by quantum feedback

Detection of a single photon escaping an optical cavity QED system prepares a nonclassical state of the electromagnetic field. The evolution of the state can be modified by changing the drive of the cavity. For the appropriate feedback, the conditional state can be captured (stabilized) and then released. This is observed by a conditional intensity measurement that shows suppression of vacuum Rabi oscillations for the length of the feedback pulse and their subsequent return.     

Collector Probe Measurements of Impurity Fluxes Injected into the Plasma of the T-10 Tokamak

It is shown that the efflux of impurities injected into the core plasma can be detected by collector probes in the scrape-off plasma. The time evolution, orientation and radial dependences of these effluxes allow to conclude on the impurity confinement in the core plasma and the scrape-off plasma. Moreover, recycling effects can also be measured.     

Komplexkatalyse: XXV. 31P-NMR-spektroskopische charakterisierung der anti- und syn-struktur von C3-substituierten η3-allylbis(triarylphosphit)-nickel(II)-hexafluorophosphat-komplexen und der mechanismus der durch [C3H5Ni(P(OPh)3)2]PF6 katalysierten 1,4-trans-polymerisation des butadiens

The reaction of the η₃-allylbis(triarylphosphite)nickel(II) complexes with butadiene under chain propagation to give the polybutadienyl complex, [3-RC₃H₄Ni(P(OAr)₃)₂]PF₆, was monitored by ³¹P NMR spectroscopy. In the case of the triphenylphosphite complex both the anti- and the syn-configuration could be identified by means of their different AB spectra. The anti-syn isomerization, the higher reactivity of the thermodynamically more stable syn-form, and the formation of the anti-structure as a result of each individual butadiene insertion step was also proved. From these observations an experimentally well-grounded mechanism of the trans regulation with the anti-syn isomerization as the rate-determining step could be derived for the first time.     

Shanzhisin methyl ester gentiobioside,a new iridoid - isolation and synthesis

The title compound 1 has been isolated from $\text{Canthium subcordatum}$ and its structure deduced; 1 was synthesised from shanzhiside methyl ester.