Comparison of Swendsen‐Wang and heat‐bath dynamics

We prove that the spectral gap of the Swendsen‐Wang process for the Potts model on graphs with bounded degree is bounded from below by some constant times the spectral gap of any single‐spin dynamics. This implies rapid mixing for the two‐dimensional Potts model at all temperatures above the critical one, as well as rapid mixing at the critical temperature for the Ising model. After this we introduce a modified version of the Swendsen‐Wang algorithm for planar graphs and prove rapid mixing for the two‐dimensional Potts models at all non‐critical temperatures. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 520–535, 2013     

On the Behavior of the Threshold Operator for Bandlimited Functions

One interesting question is how the good local approximation behavior of the Shannon sampling series for the Paley–Wiener space $\mathcal {PW}_{\pi}^{1}$ is affected if the samples are disturbed by the non-linear threshold operator. This operator, which is important in many applications, sets all samples whose absolute value is smaller than some threshold to zero. In this paper we analyze a generalization of this problem, in which not the Shannon sampling series is disturbed by the threshold operator but a more general system approximation process, were a stable linear time-invariant system is involved. We completely characterize the stable linear time-invariant systems that, for some functions in $\mathcal {PW}_{\pi}^{1}$ , lead to a diverging approximation process as the threshold is decreased to zero. Further, we show that if there exists one such function then the set of functions for which divergence occurs is in fact a residual set. We study the pointwise behavior as well as the behavior of the L ^∞-norm of the approximation process. It is known that oversampling does not lead to stable approximation processes in the presence of thresholding. An interesting open problem is the characterization of the systems that can be stably approximated with oversampling.     

Cold highly charged ions in a cryogenic Paul trap

Narrow optical transitions in highly charged ions (HCIs) are of particular interest for metrology and fundamental physics, exploiting the high sensitivity of HCIs to new physics. The highest sensitivity for a changing fine structure constant ever predicted for a stable atomic system is found in Ir^17?+?. However, laser spectroscopy of HCIs is hindered by the large (～ 10⁶ K) temperatures at which they are produced and trapped. An unprecedented improvement in such laser spectroscopy can be obtained when HCIs are cooled down to the mK range in a linear Paul trap. We have developed a cryogenic linear Paul trap in which HCIs will be sympathetically cooled by ⁹Be^?+? ions. Optimized optical access for laser light is provided while maintaining excellent UHV conditions. The Paul trap will be connected to an electron beam ion trap (EBIT) which is able to produce a wide range of HCIs. This EBIT will also provide the first experimental input needed for the determination of the transition energies in Ir^17?+?, enabling further laser-spectroscopic investigations of this promising HCI.     

Real-time electron dynamics with exact-exchange time-dependent density-functional theory

The exact exchange potential in time-dependent density-functional theory is defined as an orbital functional through the time-dependent optimized effective potential (TDOEP) method. We numerically solve the TDOEP integral equation for the real-time nonlinear intersubband electron dynamics in a semiconductor quantum well with two occupied subbands. It is found that memory effects become significant in the vicinity of intersubband resonances.     

Stark spectroscopy of excited-state transitions in a conjugated polymer

Stark spectroscopy, which is well established for probing transitions between the ground and excited states of many material classes, is extended to transitions between transient excited states. To this end, it is combined with femtosecond pump-probe spectroscopy on a conjugated polymer with appropriately introduced traps which harvest excitation energy and build up a sufficient excited state population. The results indicate a significant difference in the effective dipole moments between two short lived excited states.     

High sensitivity sensing of nitroaromatic explosive vapors based on polytriphenylamines with AIE‐active tetraphenylethylene side groups

Two polytriphenylamines (PTPAs) (P1 and P2) with aggregation induced emission (AIE)‐active tetraphenylethylene side groups have been designed and successfully synthesized. Both polymers only faintly emit in dilute solution but show strong emission in aggregated state, meaning that they are AIE‐active. The detection of 1,3,5‐trinitrobenzene (TNB) vapors has been investigated by photoluminescence (PL) quenching in polymer films. High solid state quantum yields and donor‐acceptor interactions of the electron‐rich PTPA chains with the TNB analyte, hereby, induce a high sensing sensitivity, both for P1 and P2 films towards TNB vapor. Contacting thin P1 and P2 films with saturated TNB vapor, the PL intensity was quenched by 85% for P1 and 89% for P2 within 600 s, respectively. The sensing process is reversible, >90% of the PL is recovered, also after repeated cycling. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 53, 1753–1761     

Singlet Fission in Carbene-Derived Diradicaloids

Herein, we present a new class of singlet fission (SF) materials based on diradicaloids of carbene scaffolds, namely cyclic (alkyl)(amino)carbenes (CAACs). Our modular approach allows the tuning of two key SF criteria: the steric factor and the diradical character. In turn, we modified the energy landscapes of excited states in a systematic manner to accommodate the needs for SF. We report the first example of intermolecular SF in solution by dimer self-assembly at cryogenic temperatures.     

Highly Functionalized Cyclopentane Derivatives by Tandem Michael Addition/Radical Cyclization/Oxygenation Reactions

Densely functionalized cyclopentane derivatives with up to four consecutive stereocenters are assembled by a tandem Michael addition/single‐electron transfer oxidation/radical cyclization/oxygenation strategy mediated by ferrocenium hexafluorophosphate, a recyclable, less toxic single‐electron transfer oxidant. Ester enolates were coupled with α‐benzylidene and α‐alkylidene β‐dicarbonyl compounds with switchable diastereoselectivity. This pivotal steering element subsequently controls the diastereoselectivity of the radical cyclization step. The substitution pattern of the radical cyclization acceptor enables a switch of the cyclization mode from a 5‐exo pattern for terminally substituted olefin units to a 6‐endo mode for internally substituted acceptors. The oxidative anionic/radical strategy also allows efficient termination by oxygenation with the free radical 2,2,6,6‐tetramethyl‐1‐piperidinoxyl, and two C?C bonds and one C?O bond are thus formed in the sequence. A stereochemical model is proposed that accounts for all of the experimental results and allows the prediction of the stereochemical outcome. Further transformations of the synthesized cyclopentanes are reported.