Syntheses and Crystal Structures of Rare-Earth Oxyapatites Ca2RE8(SiO4)6O2 (RE = Pr,Tb, Ho,Tm)

Journal of Chemical Crystallography - Four different rare-earth oxyapatites of Ca2RE8(SiO4)6O2 (RE?=?Pr, Tb, Ho, Tm) were synthesized using a solution-based method followed by drying,...     

Impact and quasistatic limit in the quantum-path theory of pressure broadening

The quantum-path theory of collision broadening involves a correlation function which can be calculated by infinite-order perturbation theory. From the expression obtained, both the impact and the quasistatic limit are easily derived. Application of the WKB method is discussed for the impact result.     

Quantum-state diffusion with adaptive noise

We present a scheme for stochastic quantum-state diffusion (QSD) with adaptive noise to calculate the time evolution of an arbitrary observable of an open system. The method is based on the fact that the observable is much less sensitive to adaptive noise than to noise with a random phase. Hence, the individual realisations of the expectation value of the observable stay closer to the average evolution and fewer realisations are required to obtain the ensemble average. This is illustrated by applying QSD to a driven two-level system using both randomly phased and adaptive noise. Applying QSD with adaptive noise to an undriven two-level system enables us to derive a deterministic Schr?dinger equation that produces the exact evolution of an arbitrary observable. Received: 31 July 1997 / Received in final form: 12 February 1998 / Accepted: 13 March 1998     

Duality relations and equivalences for models with O(N) and cubic symmetry

Formal expression for high-temperature series are derived for models with O(N) and cubic symmetry, with a special form of nearest neighbor interactions on the honeycomb lattice. By deriving low-temperature series for a class of generalized solid-on-solid and cubic models, a duality relation is established. Equivalences between cubic and SOS type models are also found. In the large-N limit, the series reduce to those of the hard hexagon model.     

On quantum-mechanical unified theories of collisional spectral line broadening

We compare the Baranger-type unified theory of line broadening with a quantum version of the binary-collision approach. For the simple model system of a two-state atom, where both treatments are well-defined, the binary-collision theory results only from the exact formalism after an inversion of an integration variable in an integral equation. On the other hand, the binary-collision theory is applicable to more general systems. In the limiting cases of the impact and the quasistatic theories, the two treatments yield identical results.     

Universal description of geometric phases in higher-order optical modes bearing orbital angular momentum

We study geometric phases that arise from (cyclic) transformations of the transverse spatial structure of paraxial optical modes. Our approach involves bosonic ladder operators that, in the spirit of the quantum-mechanical harmonic oscillator, generate sets of transverse optical modes. It applies to modes of all orders in a very natural way and provides a universal geometric interpretation of the phase shifts acquired by nonastigmatic modes under typical experimental conditions.     

Bis(imino)phenoxide complexes of aluminium

Reaction of Me(3)Al (one equivalent) with the bis(imino)phenol, [2,6-(ArNCH)(2)-4-MeC(6)H(2)OH] (I)(Ar = 2,6-Pr(i)(2)C(6)H(3)) in toluene at ambient temperature yields the yellow complex [Me(2)Al[2,6-(ArNCH)(2)-4-MeC(6)H(2)O]](1). Interaction of two equivalents of Me(3)Al in refluxing toluene affords the red complex [(Me(2)Al)(2)[2-ArNCH(Me)-6-(ArNCH)-4-MeC(6)H(2)O]](2). Similar interaction (two equivalents, refluxing toluene) of MeAlCl(2) or (i)Bu(3)Al with [2,6-(ArNCH)(2)-4-MeC(6)H(2)OH] affords [ClAl[2,6-(ArNCH)(2)-4-MeC(6)H(2)O](2)](3) or [(i)Bu(2)Al[2,6-(ArNCH)(2)-4-MeC(6)H(2)O]](4), respectively. Hydrolysis of 2 readily affords the iminoaminophenol ligand [2-(ArN=CH)-6-ArNHCH(Me)-4-MeC(6)H(2)OH](II), which reacts further with Me(3)Al to afford [Me(2)Al[2-ArNCH(Me)-6-(ArNCH)-4-MeC(6)H(2)O]](5). An X-ray study on reveals bidentate imino-alkoxide ligation about the distorted aluminium centre, whereas is a binuclear structure with tetrahedral aluminiums ligated by imino-alkoxide and amido-alkoxide ligand fragments, respectively. For and bidentate imino-alkoxide ligation is observed.