d-outcome measurement for a nonlocality test

For the purpose of a nonlocality test, we propose a general correlation observable of two parties by utilizing local d- outcome measurements with SU(d) transformations and classical communications. Generic symmetries of the SU(d) transformations and correlation observables are found for the test of nonlocality. It is shown that these symmetries dramatically reduce the number of numerical variables, which is important for numerical analysis of nonlocality. A linear combination of the correlation observables, which is reduced to the Clauser- Home-Shimony-Holt (CHSH) Bell's inequality for two outcome measurements, leads to the Collins-Gisin-Linden-Massar-Popescu (CGLMP) nonlocality test for d-outcome measurement. As a system to be tested for its nonlocality, we investigate a continuous- variable (CV) entangled state with d measurement outcomes. It allows the comparison of nonlocality based on different numbers of measurement outcomes on one physical system. In our example of the CV state, we find that a pure entangled state of any degree violates Bell's inequality for d(greater than or equal to2) measurement outcomes when the observables are of SU(d) transformations.

Kinetics of phase transformations in a model with metastable fluid-fluid separation: A molecular dynamics study

By molecular dynamics (MD) simulations we study the crystallization process in a model system whose particles interact by a spherical pair potential with a narrow and deep attractive well adjacent to a hard repulsive core. The phase diagram of the model displays a solid-fluid equilibrium, with a metastable fluid-fluid separation. Our computations are restricted to fairly small systems (from 2592 to 10368 particles) and cover long simulation times, with constant energy trajectories extending up to 76x10(6) MD steps. By progressively reducing the system temperature below the solid-fluid line, we first observe the metastable fluid-fluid separation, occurring readily and almost reversibly upon crossing the corresponding line in the phase diagram. The nucleation of the crystal phase takes place when the system is in the two-fluid metastable region. Analysis of the temperature dependence of the nucleation time allows us to estimate directly the nucleation free energy barrier. The results are compared with the predictions of classical nucleation theory. The critical nucleus is identified, and its structure is found to be predominantly fcc. Following nucleation, the solid phase grows steadily across the system, incorporating a large number of localized and extended defects. We discuss the relaxation processes taking place both during and after the crystallization stage. The relevance of our simulation for the kinetics of protein crystallization under normal experimental conditions is discussed. (C) 2002 American Institute of Physics.

Quantitative Analysis of Adsorbate Concentrations by Diffuse Reflectance FT-IR

Fully quantitative analyses of DRIFTS data are required when the surface concentrations and the specific rate constants of reaction (or desorption) of adsorbates are needed to validate microkinetic models. The relationship between the surface coverage of adsorbates and various functions derived from the signal collected by DRIFTS is discussed here. The Kubelka-Munk and pseudoabsorbance (noted here as absorbance, for the sake of brevity) transformations were considered, since those are the most commonly used functions when data collected by DRIFTS are reported. Theoretical calculations and experimental evidence based on the study of CO adsorption on Pt/SiO2 and formate species adsorbed on Pt/CeO2 showed that the absorbance (i.e., ) log 1/R������¢, with R������¢ ) relative reflectance) is the most appropriate, yet imperfect, function to give a linear representation of the adsorbate surface concentration in the examples treated here, for which the relative reflectance R������¢ is typically > 60%. When the adsorbates lead to a strong signal absorption (e.g., R������¢ < 60%), the Kubelka-Munk function is actually more appropriate. The absorbance allows a simple correction of baseline drifts, which often occur during time-resolved data collection over catalytic materials. Baseline corrections are markedly more complex in the case of the other mathematical transforms, including the function proposed by Matyshak and Krylov (Catal. Today 1995, 25, 1-87), which has been proposed as an appropriate representation of surface concentrations in DRIFTS spectroscopy.