Entanglement between collective operators in a linear harmonic chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several noncontiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.

Equilibrium polymerization of cyclic carbonate oligomers. III. Chain branching and the gel transition

Ring-opening polymerization of cyclic polycarbonate oligomers, where monofunctional active sites act on difunctional monomers to produce an equilibrium distribution of rings and chains, leads to a "living polymer." Monte Carlo simulations [two-dimensional (2D) and three-dimensional (3D)] of the effects of single [J. Chem. Phys. 115, 3895 (2001)] and multiple active sites [J. Chem. Phys. 116, 7724 (2002)] are extended here to trifunctional active sites that lead to branching. Low concentrations of trifunctional particles c(3) reduce the degree of polymerization significantly in 2D, and higher concentrations (up to 32%) lead to further large changes in the phase diagram. Gel formation is observed at high total density and sizable c(3) as a continuous transition similar to percolation. Polymer and gel are much more stable in 3D than in 2D, and both the total density and the value of c(3) required to produce high molecular weight aggregates are reduced significantly. The degree of polymerization in high-density 3D systems is increased by the addition of trifunctional monomers and reduced slightly at low densities and low c(3). The presence of branching makes equilibrium states more sensitive (in 2D and 3D) to changes in temperature T. The stabilities of polymer and gel are enhanced by increasing T, and-for sufficiently high values of c(3)-there is a reversible polymer-gel transformation at a density-dependent floor temperature. (C) 2002 American Institute of Physics.

Effects of n-3 long chain polyunsaturated fatty acids on depressed mood: Systematic review of published trials.

Background: Greater dietary intakes of n–3 long-chain polyunsaturated fatty acids (n–3 PUFAs) may be beneficial for depressed mood. Objective: This study aimed to systematically review all published randomized controlled trials investigating the effects of n–3 PUFAs on depressed mood. Design: Eight medical and health databases were searched over all years of records until June 2006 for trials that exposed participants to n–3 PUFAs or fish, measured depressed mood, were conducted on human participants, and included a comparison group. Results: Eighteen randomized controlled trials were identified; 12 were included in a meta-analysis. The pooled standardized difference in mean outcome (fixed-effects model) was 0.13 SDs (95% CI: 0.01, 0.25) in those receiving n–3 PUFAs compared with placebo, with strong evidence of heterogeneity (I2 = 79%, P <0.001). The presence of funnel plot asymmetry suggested that publication bias was the likely source of heterogeneity. Sensitivity analyses that excluded one large trial increased the effect size estimates but did not reduce heterogeneity. Metaregression provided some evidence that the effect was stronger in trials involving populations with major depression—the difference in the effect size estimates was 0.73 (95% CI: 0.05, 1.41; P = 0.04), but there was still considerable heterogeneity when trials that involved populations with major depression were pooled separately (I2 = 72%, P <0.001). Conclusions: Trial evidence that examines the effects of n–3 PUFAs on depressed mood is limited and is difficult to summarize and evaluate because of considerable heterogeneity. The evidence available provides little support for the use of n–3 PUFAs to improve depressed mood. Larger trials with adequate power to detect clinically important benefits are required.

DFT studies of long-chain FAMEs: theoretical justification for determining chain length and unsaturation from experimental Raman spectra

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of a series of long-chain, saturated fatty acid methyl esters (FAMEs) with the formula CH2nO2 (n = 5-21) and two series of unsaturated FAMEs. The calculations showed that the lowest energy conformer within the saturated FAMEs is the simple (all-trans) structure and, in general, it was possible to reproduce experimental data using calculations on only the all-trans conformer. The only exception was C6H12O2, where a second low-lying conformer had to be included in order to correctly simulate the experimental Raman spectrum. The objective of the work was to provide theoretical justification for the methods that are commonly used to determine the properties of the fats and oils, such as chain length and degree of unsaturation, from experimental Raman data. Here it is shown that the calculations reproduce the trends and calibration curves that are found experimentally and also allow the reasons for the failure of what would appear to be rational measurements to be understood. This work shows that although the assumption that each FAME can simply be treated as a collection of functional groups can be justified in some cases, many of the vibrational modes are complex motions of large sections of the molecules and thus would not be expected to show simple linear trends with changes in structure, such as increasing chain length and/or unsaturation. Simple linear trends obtained from experimental data may thus arise from cancellation of opposing effects, rather than reflecting an underlying simplicity.

Conformations, vibrational frequencies and Raman intensities of short-chain fatty acid methyl esters using DFT with 6-31G(d) and Sadlej pVTZ basis sets

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of three short-chain fatty acid methyl esters (FAMEs) with the formula CnH2nO2 (n = 3-5). In all three FAMEs, the lowest energy conformer has a simple 'all-trans' structure but there are other conformers, with different torsions about the backbone, which lie reasonably close in energy to the global minimum. One result of this is that the solid samples we studied do not appear to consist entirely of the lowest energy conformer. Indeed, to account for the 'extra' bands that were observed in the Raman data but were not predicted for the all-trans conformer, it was necessary to add-in contributions from other conformers before a complete set of vibrational assignments could be made. Provided this was done, the agreement between experimental Raman frequencies and 6-31G(d) values (after scaling) was excellent, RSD = 12.6 cm(-1). However, the agreement between predicted and observed intensities was much less satisfactory. To confirm the validity of the approach followed by the 6-3 1 G(d) basis set, we used a larger basis set, Sadlej pVTZ, and found that these calculations gave accurate Raman intensities and simulated spectra (summed from two different conformers) that were in quantitative agreement with experiment. In addition, the unscaled Sadlej pVTZ, and the scaled 6-3 1 G(d) calculations gave the same vibrational mode assignments for all bands in the experimental data. This work provides the foundation for calculations on longer-chain FAMEs (which are closer to those found as triglycerides in edible fats and oils) because it shows that scaled 6-3 1 G(d) calculations give equally accurate frequency predictions, and the same vibrational mode assignments, as the much more CPU-expensive Sadlej pVTZ basis set calculations.