Renormalization group and high-temperature series for the two-dimensional ising model

We employ high-temperature series to investigate a two-parameter class of renormalization group transformations for the two-dimensional Ising model on the triangular lattice. For the static case we identify an optimal organization of the high-temperature expansion and an optimal transformation matrix and thus find, in second order, =0.96 and the magnetic eigenvaluey=2-/2=1.76.From recursion relations for flip rates we find the dynamic exponent to be the same for all transformations in our two-parameter class,z=2.32.Our fixed-point flip rates do not describe a Markov process even though the corresponding master equation for the single-event probability displays no explicit memory effects. The non-Markovian nature shows up only in a violation of the Markovian detailed balance conditions.     

Renormalized perturbation theory of the Van der Pol oscillator

The renormalized perturbation expansion for the linewidth of the Van der Pol oscillator is extended to fifth order. The results of the previously obtained fourth order are thereby improved for pump strengthsa5. No indication of a breakdown of the expansion, even for strong pumping, is found.     

C-S Bond Cleavage Reactions of Sulfonediimines

Abstract

Nucleophilic C-S bond cleavage of Sulfonediimines to Sulfinamidine-type Structures is discussed     

Micro-manipulation of small particles by node position control of an ultrasonic standing wave

For the controlled positioning of small particles with ultrasound a standing wave in a fluid is used. The standing wave is implemented in a resonator, that consists of a fluid filled tube and two piezoelectric transducers on each end. A one-dimensional model of a piezo-device including the fluid-loading on one side and a backside support is introduced. This model allows the calculation of the transmitted wave as a function of the applied electric voltage and the incident wave. In addition, when an electrical impedance is connected to the piezo-device, the reflection coefficient can be varied in amplitude and phase, so that the parameters of the reflected wave can be controlled completely. The resonator itself, consisting of a piezo-device on each end and the fluid between, is included in the model. Several methods to shift the nodes of the standing wave in the resonator are investigated and the ability to position particles is discussed.     

Master-equation for the statistical operator of solid state laser

In extension of a preceding paper we derive a masterequation for the complete statistical operator of a laser model. The whole system containing atoms, field and several thermal reservoirs, the latter providing loss effects and pumping, is treated quantummechanically. The masterequation is at first solved in the selfconsistent field approximation (SCFA). The results essentially confirm those given by quasiclassical theories, including the coherence properties of the lightmode (comp. (4)). Secondly, an approximate treatment is given of particle-field correlations which go beyond the SCFA and therefore beyond the quasiclassical approach. It is shown explicitly that such correlation effects influence the coherence behavior of the lightfield, i.e. we get a further small deviation from the pure Glauber state.     

Rearrangement of 3-Acyl Derivatives of L-Ascorbic Acid

Abstract

Evidence of rearrangement of 3-acyl derivatives of ascorbic acid to 2-acyl derivatives has been found for carbon and phosphorus acyl groups. The observations are consistent with intramolecular rearrangement through a cyclic intermediate in which the acyl group is bonded to both the 2- and 3-oxygen atoms of ascorbic acid. A rate of rearrangement has been measured for the 3-diphenylphosphinate ester. Calculated results indicate an increase in negative atomic charge at O-2 in the 3-acyl esters but a decrease in the charge of O-3 in the 2-acyl esters.     

Equivalence of random and competing nonrandom bonds for Edwards Anderson spin-glass

We map the Edwards Anderson Hamiltonian onto an effective Hamiltonian for Ising spins with nonrandom competing couplings. A high-temperature series is used to calculate the coupling constants to 20th, 16th, and 12th order for two, three, and four dimensions, respectively. We conclude the lower critical dimension to be close to three and find the correlation-length and susceptibility critical exponents to be twice as large as for thed=3 Ising model.