Entropic functionals of Laguerre and Gegenbauer polynomials with large parameters

The determination of the physical entropies (R\'enyi, Shannon, Tsallis) of high-dimensional quantum systems subject to a central potential requires the knowledge of the asymptotics of some power and logarithmic integral functionals of the hypergeometric orthogonal polynomials which control the wavefunctions of the stationary states. For the $D$-dimensional hydrogenic and oscillator-like systems, the wavefunctions of the corresponding bound states are controlled by the Laguerre ($\mathcal{L}_{m}^{(\alpha)}(x)$) and Gegenbauer ($\mathcal{C}^{(\alpha)}_{m}(x)$) polynomials in both position and momentum spaces, where the parameter $\alpha$ linearly depends on $D$. In this work we study the asymptotic behavior as $\alpha \to \infty$ of the associated entropy-like integral functionals of these two families of hypergeometric polynomials

Entanglement and the Born-Oppenheimer approximation in an exactly solvable quantum many-body system

We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons". We study the dependence of entanglement on the inter-particle interaction strength, on the number of particles, and on the particle masses. Consistent with kinematic intuition, the entanglement between two subsystems vanishes when the subsystems have very different masses, while it attains its maximal value for subsystems of comparable mass. We show how this entanglement feature can be inferred by means of the Born-Oppenheimer Ansatz, whose validity and breakdown can be understood from a quantum information point of view.Comment: Accepted in Eur. Phys. J. D (2014

Negative refraction and energy funneling by hyperbolic materials: An experimental demonstration in acoustics

This Letter reports the design, fabrication, and experimental characterization of hyperbolic materials showing negative refraction and energy funneling of airborne sound. Negative refraction is demonstrated using a stack of five holey Plexiglas plates where their thicknesses, layer separation, hole diameters, and lattice periodicity have been determined to show hyperbolic dispersion around 40 kHz. The resulting hyperbolic material shows a flat band profile in the equifrequency contour allowing the gathering of acoustic energy in a broad range of incident angles and its funneling through the material. Our demonstrations foresee interesting developments based on both phenomena. Acoustic imaging with subwavelength resolution and spot-size converters that harvest and squeeze sound waves irradiating from many directions into a collimated beam are just two possible applications among many.This work was partially supported by the Office of Naval Research (USA) under Grant No. N000140910554, and by the Ministerio de Economia y Competitividad (Spain) under Contract No. TEC2010-19751. J. C. gratefully acknowledges financial support from the Danish Council for Independent Research and a Sapere Aude Grant (12-134776).García Chocano, VM.; Christensen, J.; Sánchez-Dehesa Moreno-Cid, J. (2014). Negative refraction and energy funneling by hyperbolic materials : an experimental demonstration in acoustics. Physical Review Letters. 112(14). https://doi.org/10.1103/PhysRevLett.112.144301S1121

Noise control by sonic crystal barriers made of recycled materials

A systematic study of noise barriers based on sonic crystals made of cylinders that use recycled materials like absorbing component is here reported. The barriers consist of only three rows of perforated metal shells filled with rubber crumb. Measurements of reflectance and transmittance by these barriers are reported. Their attenuation properties result from a combination of sound absorption by the rubber crumb and reflection by the periodic distribution of scatterers. It is concluded that porous cylinders can be used as building blocks whose physical parameters can be optimized in order to design efficient barriers adapted to different noisy environments

Quantum-information entropies for highly excited states of single-particle systems with power-type potentials

The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x^2k with k∈N and x∈R, is investigated in the position and momentum spaces within the semiclassical (WKB) approximation. It is found that for highly excited states both physical entropies, as well as their sum, have a logarithmic dependence on its quantum number not only when k=1 (harmonic oscillator), but also for any fixed k. As a by-product, the extremal case k→∞ (the infinite well potential) is also rigorously analyzed. It is shown that not only the position-space entropy has the same constant value for all quantum states, which is a known result, but also that the momentum-space entropy is constant for highly excited states

Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal

In this paper, we report experiments on the scattering of surface-elastic waves by a periodic array of cylindrical holes. The experiments were performed in a marble quarry by drilling cylindrical holes in two different configurations: honeycomb and triangular lattices. The attenuation spectra of the surface waves show the existence of absolute band gaps for elastic waves in these semi-infinite two-dimensional crystals. Results are compared with theoretical calculations based on a scalar-wave approach. The scaling property of the underlying theory has led us to explore the possible application of the results obtained to the attenuation of surface waves in seismic movements.This work was partially supported by the Comisión Interministerial de Ciencia y Tecnología of Spain, Contract No. MAT97-0698-C04. We also thank the Consejo Superior de Investigaciones Científicas for the special funding to perform this experiment.Peer reviewe

Developmental Instability and Fitness in Periploca laevigata Experiencing Grazing Disturbance

10 páginas, 4 figuras, 4 tablas.We investigated the sensitivity of developmental instability measurements (leaf fluctuating asymmetry, floral radial asymmetry, and shoot translational asymmetry) to a long‐standing natural stress (grazing) in a palatable tannin‐producing shrub (Periploca laevigata Aiton). We also assessed the relationship between these measures of developmental instability and fitness components (growth and floral production). Developmental instability, measured by translational asymmetry, was the most accurate estimator of a plant’s condition and, consequently, environmental stress. Plants with less translational asymmetry grew more and produced more flowers. Plants from the medium‐grazed population were developmentally more stable, as estimated by translational and floral asymmetry, than either more heavily or more lightly grazed populations. Leaf fluctuating asymmetry was positively correlated with tannin concentration. The pattern of internode growth also responded to grazing impact. Plants under medium to heavy grazing pressure accelerated early growth and consequently escaped herbivory later in the season, i.e., at the beginning of the spring, when grazing activity was concentrated in herbaceous plants. Periploca laevigata accelerated growth and finished growing sooner than in the other grazing treatment. Thus, its annual growth was more mature and less palatable later in the season when grazers typically concentrate on shrubs. The reduction of developmental instability under medium grazing is interpreted as a direct effect of grazing and not as the release from competition.The work was realized under the Desertification Risk Assessment in Silvopastoral Mediterranean Ecosystems (DRASME) collaborative research project. DRASME is funded by the European Community under its International Cooperation with Developing Countries Program, contract number ERBIC18‐CT98‐0392. The support from this program is gratefully acknowledged. We are grateful to Dr. T. Navarro and Dr. M. Vrahnakis for critically reading the manuscript and making helpful suggestions. David Navas and Antonio Gonzalez assigned the taxonomic identification of each species, for which we are very grateful. We thank Rosa Jimenez Ortega, Antonio Parra Perez, David Navas, and Antonio Gonzalez for collaborating with us in the collection of data.Peer reviewe