Quantum hamiltonians and prime numbers

A short review of Schroedinger hamiltonians for which the spectral problem has been related in the literature to the distribution of the prime numbers is presented here. We notice a possible connection between prime numbers and centrifugal inversions in black holes and suggest that this remarkable link could be directly studied within trapped Bose-Einstein condensates. In addition, when referring to the factorizing operators of Pitkanen and Castro and collaborators, we perform a mathematical extension allowing a more standard supersymmetric approachComment: 10 pages, 2 figures, accepted as a Brief Review at MPL

Subwavelength fractional Talbot effect in layered heterostructures of composite metamaterials

We demonstrate that under certain conditions, fractional Talbot revivals can occur in heterostructures of composite metamaterials, such as multilayer positive and negative index media, metallodielectric stacks, and one-dimensional dielectric photonic crystals. Most importantly, without using the paraxial approximation we obtain Talbot images for the feature sizes of transverse patterns smaller than the illumination wavelength. A general expression for the Talbot distance in such structures is derived, and the conditions favorable for observing Talbot effects in layered heterostructures is discussed.Comment: To be published in Phys. Rev.

The Effects of Childhood Social Support and Family Resiliency on Mental Health in Adulthood

The effect of social support on the overall health and quality of life in adulthood has been well documented particularly in chronic disease populations. Very few studies examined the relationships between childhood social support, family resiliency and mental health in adulthood in the community and among disadvantaged minority populations. We examined the role of social support and family resilience during childhood on subsequent mental health-related quality of life (HRQoL) in adulthood among racial/ethnic minorities. A needs assessment survey which was designed to explore health determinants and quality of life indicators using a community-based participatory research (CBPR) approach in a low-income community in Tampa was analyzed. Participants were predominantly low-income non-Hispanic black and Hispanic population (n=187). The outcome mental HRQoL was measured using the validated Centers for Disease Control and Prevention’s (CDC) “Healthy Days Measure” instrument. We utilized sequential multivariable logistic regression models to examine the independent effects of childhood social support and family resiliency on mental HRQoL in adulthood. Approximately 12.3% of study participants reported poor mental HRQoL (i.e. ≥14 unhealthy days due to mental health). Childhood social support and family resiliency were significant predictors of mental HRQoL in adulthood, after controlling for sociodemographic characteristics. Sleep and composite health issues in adulthood were also associated with mental HRQoL. Our analyses highlight an opportunity to promote mental health through support of interventions that improve positive family relationships and reduce the burden of chronic health issues among non-Hispanic black and Hispanic children

Crystallization of Carbon Oxygen Mixtures in White Dwarf Stars

We determine the phase diagram for dense carbon/ oxygen mixtures in White Dwarf (WD) star interiors using molecular dynamics simulations involving liquid and solid phases. Our phase diagram agrees well with predictions from Ogata et al. and Medin and Cumming and gives lower melting temperatures than Segretain et al. Observations of WD crystallization in the globular cluster NGC 6397 by Winget et al. suggest that the melting temperature of WD cores is close to that for pure carbon. If this is true, our phase diagram implies that the central oxygen abundance in these stars is less than about 60%. This constraint, along with assumptions about convection in stellar evolution models, limits the effective S factor for the $^{12}$C($\alpha,\gamma$)$^{16}$O reaction to S_{300} <= 170 keV barns.Comment: 4 pages, 2 figures, Phys. Rev. Lett. in pres

Neutrino Scattering in Heterogeneous Supernova Plasmas

Neutrinos in core collapse supernovae are likely trapped by neutrino-nucleus elastic scattering. Using molecular dynamics simulations, we calculate neutrino mean free paths and ion-ion correlation functions for heterogeneous plasmas. Mean free paths are systematically shorter in plasmas containing a mixture of ions compared to a plasma composed of a single ion species. This is because neutrinos can scatter from concentration fluctuations. The dynamical response function of a heterogeneous plasma is found to have an extra peak at low energies describing the diffusion of concentration fluctuations. Our exact molecular dynamics results for the static structure factor reduce to the Debye Huckel approximation, but only in the limit of very low momentum transfers.Comment: 11 pages, 13 figure

Diffusion of Neon in White Dwarf Stars

Sedimentation of the neutron rich isotope $^{22}$Ne may be an important source of gravitational energy during the cooling of white dwarf stars. This depends on the diffusion constant for $^{22}$Ne in strongly coupled plasma mixtures. We calculate self-diffusion constants $D_i$ from molecular dynamics simulations of carbon, oxygen, and neon mixtures. We find that $D_i$ in a mixture does not differ greatly from earlier one component plasma results. For strong coupling (coulomb parameter $\Gamma>$ few), $D_i$ has a modest dependence on the charge $Z_i$ of the ion species, $D_i \propto Z_i^{-2/3}$. However $D_i$ depends more strongly on $Z_i$ for weak coupling (smaller $\Gamma$). We conclude that the self-diffusion constant $D_{\rm Ne}$ for $^{22}$Ne in carbon, oxygen, and neon plasma mixtures is accurately known so that uncertainties in $D_{\rm Ne}$ should be unimportant for simulations of white dwarf cooling.Comment: 6 pages, 5 figures, minor changes, Phys. Rev. E in pres

Spectral Statistics and Dynamical Localization: sharp transition in a generalized Sinai billiard

We consider a Sinai billiard where the usual hard disk scatterer is replaced by a repulsive potential with $V(r)\sim\lambda r^{-\alpha}$ close to the origin. Using periodic orbit theory and numerical evidence we show that its spectral statistics tends to Poisson statistics for large energies when $\alpha2$, while for $\alpha=2$ it is independent of energy, but depends on $\lambda$. We apply the approach of Altshuler and Levitov [Phys. Rep. {\bf 288}, 487 (1997)] to show that the transition in the spectral statistics is accompanied by a dynamical localization-delocalization transition. This behaviour is reminiscent of a metal-insulator transition in disordered electronic systems.Comment: 8 pages, 2 figures, accepted for publication in Phys. Rev. Let

Productivity of Florida Springs: Second annual report to Biology Branch, Office of Naval Research progress from January 1 to December 31, 1954

Production measurements at different times of the year indicate a linear relationship of light intensity and overall production at about 8% of the visible light energy reaching plant level. Measurements of a coral reef at Eniwetok indicate 6%. Further evidence of breeding at all seasons but with a quantitative pulse in the seasons of maximum light indicates that the seasonal fluctuation in primary production is routed through reproduction rather than through major changes in populations. The succession of plants and anmals of the aufwuchs has been shown with glass slides and counts from Sagittaria blades. Losss of oxygen bubbles during the day and emergence of aquatic insects at night have been measured with funnels. Bell jar measurements are reported for bacterial metabolism on mud surfaces. pH determined CO2 uptake agrees with titration determinations. A few rough estimates of herbivore production have been made from caged snails, aufwuchs succession, and fish tagging. Nitrate uptake a night by aufwuchs communities has been confirmed in a circulating microcosm experiment as well as in bell jars in the springs. Distributions of oxygen and organisms have been used to criticize the saprobe stream classification system. Theoretical consideration of maximum photosynthetic rates in teh literature data indicates logarithmic rate variation inversely with organismal size just as for respiratory metabolism. Extreme pyramid shapes are thus shown for communities in which organismal size decreases up the food chain and for other communities with the same energy influx but with organismal size increasing up the food chain. Literature data is used to further demonstrate the validity of the optimum efficiency-maximum power principle for photosynthesis. Work on plants by Dr. Delle Natelson indicates essential stability of aquatic plant communities after 3 years and about 10-20% reproducibility in previous biomass estimates by Davis. Work on an animal picture of the fishery characteristics by Caldwell, Barry, and Odum is half completed. The study of aquatic insects in relationship to spring gradients by W.C. Sloan has been completed an an M.S. thesis. J. Yount has begun a study of affect of total productivity on community composition using aufwuchs organisms on glass slides placed in different current and light conditions in Silver Springs. (49pp.

Talbot effect in cylindrical waveguides

We extend the theory of Talbot revivals for planar or rectangular geometry to the case of cylindrical waveguides. We derive a list of conditions that are necessary to obtain revivals in cylindrical waveguides. A phase space approach based on the Wigner and the Kirkwood-Rihaczek functions provides a pictorial representation of TM modes interference associated with the Talbot effect