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.