Quantum chaos: an introduction via chains of interacting spins-1/2

We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts are not chaotic. The spectrum of the first exhibits repulsion of the energy levels. This is one of the main signatures of quantum chaos. We show how level repulsion develops in one-dimensional systems of interacting spins 1/2 which are devoid of random elements and involve only two-body interactions. In addition to the statistics of the eigenvalues, we analyze how the structure of the eigenstates may indicate chaos. The programs used to obtain the data are available online.Comment: 7 pages, 3 figure

Reversing non-local transport through a superconductor by electromagnetic excitations

Superconductors connected to normal metallic electrodes at the nanoscale provide a potential source of non-locally entangled electron pairs. Such states would arise from Cooper pairs splitting into two electrons with opposite spins tunnelling into different leads. In an actual system the detection of these processes is hindered by the elastic transmission of individual electrons between the leads, yielding an opposite contribution to the non-local conductance. Here we show that electromagnetic excitations on the superconductor can play an important role in altering the balance between these two processes, leading to a dominance of one upon the other depending on the spatial symmetry of these excitations. These findings allow to understand some intriguing recent experimental results and open the possibility to control non-local transport through a superconductor by an appropriate design of the experimental geometry.Comment: 6 pages, 3 figure

Final-state interaction phase difference in J/ψ→ρηJ/\psi\to\rho\eta and ωη\omega\eta decays

It is shown that the study of the $\omega-\rho^0$ interference pattern in the $J/\psi\to (\rho^0+\omega)\eta\to\pi^+\pi^-\eta$ decay provides the evidence for the large (nearly $90^\circ$) relative phase between the one-photon and the three-gluon decay amplitudes.Comment: 5 pages, revtex, \tightenlines, a version published in Phys. Rev. D 61, 117504 (2000

A Molecular Platinum Cluster Junction: A Single-Molecule Switch

We present a theoretical study of the electronic transport through single-molecule junctions incorporating a Pt6 metal cluster bound within an organic framework. We show that the insertion of this molecule between a pair of electrodes leads to a fully atomically engineered nano-metallic device with high conductance at the Fermi level and two sequential high on/off switching states. The origin of this property can be traced back to the existence of a HOMO which consists of two degenerate and asymmetric orbitals, lying close in energy to the Fermi level of the metallic leads. Their degeneracy is broken when the molecule is contacted to the leads, giving rise to two resonances which become pinned close to the Fermi level and display destructive interference.Comment: 4 pages, 4 figures. Reprinted (adapted) with permission from J. Am. Chem. Soc., 2013, 135 (6), 2052. Copyright 2013 American Chemical Societ

Effects of habitat and land use on breeding season density of male Asian Houbara Chlamydotis macqueenii

Landscape-scale habitat and land-use influences on Asian Houbara Chlamydotis macqueenii (IUCN Vulnerable) remain unstudied, while estimating numbers of this cryptic, low-density, over-hunted species is challenging. In spring 2013, male houbara were recorded at 231 point counts, conducted twice, across a gradient of sheep density and shrub assemblages within 14,300 km² of the Kyzylkum Desert, Uzbekistan. Four sets of models related male abundance to: (1) vegetation structure (shrub height and substrate); (2) shrub assemblage; (3) shrub species composition (multidimensional scaling); (4) remote-sensed derived land-cover (GLOBCOVER, 4 variables). Each set also incorporated measures of landscape rugosity and sheep density. For each set, multi-model inference was applied to generalised linear mixed models of visit-specific counts that included important detectability covariates and point ID as a random effect. Vegetation structure received strongest support, followed by shrub species composition and shrub assemblage, with weakest support for the GLOBCOVER model set. Male houbara numbers were greater with lower mean shrub height, more gravel and flatter surfaces, but were unaffected by sheep density. Male density (mean 0.14 km-2, 95% CI, 0.12‒0.15) estimated by distance analysis differed substantially among shrub assemblages, being highest in vegetation dominated by Salsola rigida (0.22 [CI, 0.20‒0.25]), high in areas of S. arbuscula and Astragalus (0.14 [CI, 0.13‒0.16] and 0.15 [CI, 0.14‒0.17] respectively), lower (0.09 [CI, 0.08‒0.10]) in Artemisia and lowest (0.04 [CI, 0.04‒0.05]) in Calligonum. The study area was estimated to hold 1,824 males (CI: 1,645‒2,030). The spatial distribution of relative male houbara abundance, predicted from vegetation structure models, had the strongest correspondence with observed numbers in both model-calibration and the subsequent year’s data. We found no effect of pastoralism on male distribution but potential effects on nesting females are unknown. Density differences among shrub communities suggest extrapolation to estimate country- or range-wide population size must take account of vegetation composition

Interference in the reaction e+e−→γπ+π−e^+e^-\to\gamma\pi^+\pi^- and the final state interaction

We describe the interference between amplitudes $e^ + e^-\to\rho\to\gamma\pi^+\pi^-$ and $e^ + e^-\to\phi\to\gamma (f_0 + \sigma) \to\gamma\pi^ + \pi^-$, with regard to the phase of the elastic $\pi\pi$ scattering background and mixing of the $f_0$ and $\sigma$ mesons. It is shown that the Fermi-Watson theorem for the final state interaction in the reaction $e^ + e^-\to\rho\to\gamma\pi^ + \pi^-$ is not valid in the case of soft photons, $\omega < 100$ MeV, in the $\phi$ meson region. The interference patterns in the spectrum of the photon energy differential cross-section and in the full cross-section as a function of the beam energy are obtained.Comment: 10 pages, revtex, 2 ps files of figure

Effects of habitat and livestock on nest productivity of the Asian houbara Chlamydotis macqueenii in Bukhara Province, Uzbekistan

To inform population support measures for the unsustainably hunted Asian houbara Chlamydotis macqueenii (IUCN Vulnerable) we examined potential habitat and land-use effects on nest productivity in the Kyzylkum Desert, Uzbekistan. We monitored 177 nests across different semi-arid shrub assemblages (clay-sand and salinity gradients) and a range of livestock densities (0–80 km-2). Nest success (mean 51.4%, 95% CI 42.4–60.4%) was similar across four years; predation caused 85% of those failures for which the cause was known, and only three nests were trampled by livestock. Nesting begins within a few weeks of arrival when food appears scarce, but later nests were more likely to fail owing to the emergence of a key predator, suggesting foraging conditions on wintering and passage sites may be important for nest productivity. Nest success was similar across three shrub assemblages and was unrelated to landscape rugosity, shrub frequency or livestock density, but was greater with taller mean shrub height (range 13–67 cm) within 50 m. Clutch size (mean = 3.2 eggs) and per-egg hatchability in successful nests (87.5%) did not differ with laying date, shrub assemblage or livestock density. We therefore found no evidence that livestock density reduced nest productivity across the range examined, while differing shrub assemblages appeared to offer similar habitat quality. Asian houbara appear well-adapted to a range of semi-desert habitats and tolerate moderate disturbance by pastoralism. No obvious in situ mitigation measures arise from these findings, leaving regulation and control as the key requirement to render hunting sustainable

Search for the scalar a0a_0 and f0f_0 mesons in the reactions e+e−→γπ0π0(η)e^+e^-\to\gamma\pi^0\pi^0(\eta)

It is shown that the reactions $e^+e^-\to\gamma\pi^0\pi^0(\eta)$ give a good chance for observing scalar $a_0$ and $f_0$ mesons. In the photon energy region less then 100 MeV the vector meson contributions $e^+e^-\to V^0\to\pi^0 V'^0\to\gamma\pi^0\pi^0(\eta)$ are negligible in comparison with the scalar mesons $e^+e^-\to\phi\to\gamma f_0(a_0)\to\gamma\pi^0\pi^0(\eta)$ for $BR(\phi\to\gamma f_0(a_0)\to\gamma\pi^0\pi^0(\eta))$ greater than $5\cdot10^{-6}(10^{-5})$. Using two-channel treatment of the $\pi\pi$ scattering the predictions for $BR(\phi\to\gamma (f_0+\sigma)\to\gamma\pi\pi)$ are derived. The four quark model, the model of $K\bar K$ molecule and the$s\bar s$ model of scalar $f_0$ and $a_0$ mesons are discussed.Comment: 31 pages, 10 ps files of figures, minor numerical changes, Appendix corrected, to be published in Phys.Rev.