Persistence vectors and higher moment tensors of polyoxyalkanes

Statistical mechanical averages of vectors and tensors characterizing the spatial configurations of polyoxymethylene (POM) and polyoxyethylene (POE) chains, i.e., the chain vector r connecting the ends of the chain and the tensors formed from this vector, are evaluated in internal reference frames attached to the first two bonds of each chain as functions of its length. Convergences of the persistence vectors a ≡ 〈 r 〉 with chain length to their limits a _∞ are delineated. For POE, the orientation of a _∞ with respect to the X₁ axes (the direction of the first bond) depends markedly on the choice of the initial bond and hence also on the internal frame of reference. Cartesian tensors up to fourth rank formed from the displacement vector ρ = r ? a are evaluated for n = 4–1922 bonds for POM and n = 3–300 bonds for POE. The second moment tensor 〈ρρ^T〉 calculated for POM is nearly cylindrically symmetric about the axis perpendicular to the plane of the first two bonds. Corresponding symmetry is absent in POE. Correlation with the freely jointed chain is investigated for the components of the tensors of fourth rank formed from the reduced vector \documentclass{article}\pagestyle{empty}\begin{document} $\tilde \rho = \left\langle {\rho \rho ^{\rm T} } \right\rangle ^{ - 1/2} \rho $\end{document}. Use of the equivalent chain model for this purpose is validated for POE but not for POM, even at n = 2000 bonds. At the limit 1/n = 0, the parameter m, representing the number of bonds of the real chain equivalent to one of the model, is estimated to be ca. 31 for POM. For POE a value of m = 10.3 ± 1.3 holds for n > 20 for all components. Results are compared with those calculated previously for polymethylene, poly(dimethylsiloxane) and polypeptides. The fact that values of m derived by analysis of moments are larger than those obtained in the usual manner by fitting the model chain to 〈r²〉₀ and r_max for the real chain demonstrates the inadequacy of artificial models for the representation of the real chain.     

ππ scattering in the I = 2 channel

I=2π⁺π⁺ scattering is studied in π⁺p reactions at 5.45 GeV/c. The π⁺π⁺ cross sections and phase shifts have been determined from the reaction π⁺p → π⁺π⁺n using first a pure and then a modified Chew-Low extrapolation to the pion pole.     

Entanglement of a photon and a collective atomic excitation

We describe a new experimental approach to probabilistic atom-photon (signal) entanglement. Two qubit states are encoded as orthogonal collective spin excitations of an unpolarized atomic ensemble. After a programmable delay, the atomic excitation is converted into a photon (idler). Polarization states of both the signal and the idler are recorded and are found to be in violation of the Bell inequality. Atomic coherence times exceeding several microseconds are achieved by switching off all the trapping fields--including the quadrupole magnetic field of the magneto-optical trap--and zeroing out the residual ambient magnetic field.     

Quantum-noise-initiated symmetry breaking of spatial solitons

The spectra of chi(2) spatial solitons are measured close to the soliton-formation threshold and show the presence of sidebands, shifted by 39 THz from the laser line. By comparing with the predictions of a quantum optical field model, solved numerically in the full (3 + 1)-dimensional space, it is claimed that the observed temporal instability of the spatial soliton is seeded by vacuum state fluctuations of the electromagnetic field.     

A homologous series of regioselectively tetradeprotonated group 8 metallocenes: new inverse crown ring compounds synthesized via a mixed sodium-magnesium tris(diisopropylamide) synergic base

Subjecting ferrocene, ruthenocene, or osmocene to the synergic amide base sodium-magnesium tris(diisopropylamido) affords a unique homologous series of metallocene derivatives of general formula [(M(C(5)H(3))(2))Na(4)Mg(4)(i-Pr(2)N)(8)] (where M = Fe (1), Ru (2), or Os (3)). X-ray crystallographic studies of 1-3 reveal a common molecular "inverse crown" structure comprising a 16-membered [(NaNMgN)(4)](4+) "host" ring and a metallocenetetraide [M(C(5)H(3))(2)](4-) "guest" core, the cleaved protons of which are lost selectively from the 1, 1', 3, and 3'-positions. Variable-temperature NMR spectroscopic studies indicate that 1, 2, and 3 each exist as two distinct interconverting conformers in arene solution, the rates of exchange of which have been calculated using coalescence and EXSY NMR measurements.     

Isolation and characterisation of the mixed-metal alkyl amide [(TMEDA)Na(mu-Bu)(mu-TMP)Mg(TMP)], an unexpected chelate-trapped intermediate in the formation of inverse crowns

Only two-fold amination occurs when 3 molar equivalents of TMPH are offered to a 1:1 BuNa-Bu2Mg mixture; adding TMEDA gives the mixed alkyl amide [(TMEDA)Na(mu-Bu)(mu-TMP)Mg(TMP)], which itself affords the phenyl-bridged analogue when reacted with benzene.     

Instability of Interfaces in the Antiferromagnetic XXZ Chain at Zero Temperature

 For the antiferromagnetic, highly anisotropic XZ and XXZ quantum spin chains, we impose periodic boundary conditions on chains with an odd number of sites to force an interface (or kink) into the chain. We prove that the energy of the interface depends on the momentum of the state. This shows that at zero temperature the interface in such chains is not stable. This is in contrast to the ferromagnetic XXZ chain for which the existence of localized interface ground states has been proven for any amount of anisotropy in the Ising-like regime. Received: 15 August 2002 / Accepted: 8 January 2003 Published online: 14 April 2003 RID="⋆" ID="⋆" ? Copyright rests with the authors. Reproduction of the entire article for non-commercial purposes is permitted. Communicated by M. Aizenman