On reduced density matrices for disjoint subsystems

We show that spin and fermion representations for solvable quantum chains lead in general to different reduced density matrices if the subsystem is not singly connected. We study the effect for two sites in XX and XY chains as well as for sublattices in XX and transverse Ising chains.Comment: 10 pages, 4 figure

Cyclic and ruled Lagrangian surfaces in complex Euclidean space

We study those Lagrangian surfaces in complex Euclidean space which are foliated by circles or by straight lines. The former, which we call cyclic, come in three types, each one being described by means of, respectively, a planar curve, a Legendrian curve of the 3-sphere or a Legendrian curve of the anti de Sitter 3-space. We also describe ruled Lagrangian surfaces. Finally we characterize those cyclic and ruled Lagrangian surfaces which are solutions to the self-similar equation of the Mean Curvature Flow. Finally, we give a partial result in the case of Hamiltonian stationary cyclic surfaces

Spectroscopic characterization of the oxo-transfer reaction from a bis(µ-oxo)dicopper(III) complex to triphenylphosphine

The oxygen-atom transfer reaction from the bis(µ-oxo)dicopper(III) complex [CuIII2(µ-O)2(L)2]2+1, where L =N,N,N,N -tetraethylethylenediamine, to PPh3 has been studied by UV-vis, EPR, 1H NMR and Cu K-edge X-ray absorption spectroscopy in parallel at low temperatures (193 K) and above. Under aerobic conditions (excess dioxygen), 1 reacted with PPh3, giving OPPh3 and a diamagnetic species that has been assigned to an oxo-bridged dicopper(II) complex on the basis of EPR and Cu K-edge X-ray absorption spectroscopic data. Isotope-labeling experiments (18O2) established that the oxygen atom incorporated into the triphenylphosphine oxide came from both complex 1 and exogenous dioxygen. Detailed kinetic studies revealed that the process is a third-order reaction; the rate law is first order in both complex 1 and triphenylphosphine, as well as in dioxygen. At temperatures above 233 K, reaction of 1 with PPh3 was accompanied by ligand degradation, leading to oxidative N-dealkylation of one of the ethyl groups. By contrast, when the reaction was performed in the absence of excess dioxygen, negligible substrate (PPh3) oxidation was observed. Instead, highly symmetrical copper complexes with a characteristic isotropic EPR signal at g= 2.11 were formed. These results are discussed in terms of parallel reaction channels that are activated under various conditions of temperature and dioxygen

Determining the strange and antistrange quark distributions of the nucleon

The difference between the strange and antistrange quark distributions, \delta s(x)=s(x)-\sbar(x), and the combination of light quark sea and strange quark sea, \Delta (x)=\dbar(x)+\ubar(x)-s(x)-\sbar(x), are originated from non-perturbative processes, and can be calculated using non-perturbative models of the nucleon. We report calculations of $\delta s(x)$ and $\Delta(x)$ using the meson cloud model. Combining our calculations of $\Delta(x)$ with relatively well known light antiquark distributions obtained from global analysis of available experimental data, we estimate the total strange sea distributions of the nucleon.Comment: 4 pages, 3 figures; talk given by F.-G. at QNP0

Estimating the impact of whaling on global whale watching

After the commercial whaling moratorium was enacted in 1986, whale watching became one of the fastest growing tourism industries worldwide. As whaling was regarded as an activity incompatible with whale watching, the possible resumption of commercial whaling caused an urgent need to investigate the potential negative effects of whaling on the whale-watching industry. We examine the potential impacts of whaling on the global whale-watching tourism industry using unbalanced panel data model. The empirical results indicate that the resumption of commercial whaling has the potential for a negative effect on the global whale-watching industry, especially for nations that are engaged in whaling.delay-difference equation model;global whale watching;whaling

Are Giant Planets Forming Around HR 4796A?

We have obtained FUSE and HST STIS spectra of HR 4796A, a nearby 8 Myr old main sequence star that possesses a dusty circumstellar disk whose inclination has been constrained from high resolution near-infrared observations to be ~17 deg from edge-on. We searched for circumstellar absorption in the ground states of C II at 1036.3 A, O I at 1039.2 A, Zn II at 2026.1 A, Lyman series H2, and CO (A-X) and failed to detect any of these species. We place upper limits on the column densities and infer upper limits on the gas masses assuming that the gas is in hydrostatic equilibrium, is well-mixed, and has a temperature, Tgas ~ 65 K. Our measurements suggest that this system possesses very little molecular gas. Therefore, we infer an upper limit for the gas:dust ratio (<4.0) assuming that the gas is atomic. We measure less gas in this system than is required to form the envelope of Jupiter.Comment: 10 pages, 3 figures (including 1 color figure), accepted for publication in Ap