Operational Gaussian Schmidt-Number Witnesses

The general class of Gaussian Schmidt-number witness operators for bipartite systems is studied. It is shown that any member of this class is reducible to a convex combination of two types of Gaussian operators using local operations and classical communications. This gives rise to a simple operational method, which is solely based on measurable covariance matrices of quantum states. Our method bridges the gap between theory and experiment of entanglement quantification. In particular, we certify lower bounds of the Schmidt number of squeezed thermal and phase-randomized squeezed vacuum states, as examples of Gaussian and non-Gaussian quantum states, respectively.Comment: 9 pages, 4 figure

Optimal Simple Rules for Fiscal Policy in a Monetary Union

The paper discusses the stabilizing potential of fiscal policy in a dynamic general-equilibrium model of monetary union. We consider a small open economy inside the currency area. We analyze the demand and supply effects of direct taxation, indirect taxation and government spending and derive optimal simple rules for fiscal stabilization of a technology shock. Fiscal policy achieves substantial macroeconomic stabilization. Simple public-expenditure rules show the highest degree of both output and inflation stabilization. The implementation lag substantially weakens output stabilization, but hardly affects the stabilization of prices. Out-put-oriented rules imply less instrument inertia than inflation-dominated rules. The implemen-tation lag leads to higher coefficients for inflation relative to output in the optimal rule. Com-pared to the single-instrument approach the simultaneous optimization of two instrument rules implies only little additional stabilization gains.Fiscal policy, monetary union, simple policy rules

NMR Studies on the Temperature-Dependent Dynamics of Confined Water

We use $^2$H NMR to study the rotational motion of supercooled water in silica pores of various diameters, specifically, in the MCM-41 materials C10, C12, and C14. Combination of spin-lattice relaxation, line-shape, and stimulated-echo analyses allows us to determine correlation times in very broad time and temperature ranges. For the studied pore diameters, 2.1-2.9 nm, we find two crossovers in the temperature-dependent correlation times of liquid water upon cooling. At 220-230 K, a first kink in the temperature dependence is accompanied by a solidification of a fraction of the confined water, implying that the observed crossover is due to a change from bulk-like to interface-dominated water dynamics, rather than to a liquid-liquid phase transition. Moreover, the results provide evidence that $\alpha$ process-like dynamics is probed above the crossover temperature, whereas $\beta$ process-like dynamics is observed below. At 180-190 K, we find a second change of the temperature dependence, which resembles that reported for the $\beta$ process of supercooled liquids during the glass transition, suggesting a value of $T_g\!\approx\!185$ K for interface-affected liquid water. In the high-temperature range, $T\!>\!225$ K, the temperature dependence of water reorientation is weaker in the smaller C10 pores than in the larger C12 and C14 pores, where it is more bulk-like, indicating a significant effect of the silica confinement on the $\alpha$ process of water in the former 2.1 nm confinement. By contrast, the temperature dependence of water reorientation is largely independent of the confinement size and described by an Arrhenius law with an activation energy of $E_a\!\approx\!0.5\$eV in the low-temperature range, $T\!<\!180$K, revealing that the confinement size plays a minor role for the $\beta$ process of water.Comment: 12 pages, 9 figure