Allometry of Workers of the Fire Ant, Solenopsis invicta

The relationship between worker body size and the shape of their body parts was explored in the polymorphic ant, Solenopsis invicta. The data consisted of 20 measurements of body parts as well as sums of some of these measurements. Size-free shape variables were created by taking the ratios of relevant measures. After log-transformation, these ratios were regressed against the logarithm of total body length, or against the log of the size of the parent part. Slopes of zero indicated that shape did not change with size, and non-zero slopes signaled a size-related change of shape. Across the range of worker sizes, the head length retained a constant proportion to body length, but relative headwidth increased such that head shape changed from a barrel-profile to a somewhat heart-shaped profile. Antennae became relatively smaller, with the club contributing more to this decline than the other parts. The alinotum became relatively shorter and higher (more humped), and the gaster increased in both relative width and length, and therefore in volume. All three pairs of legs were isometric to body length. The component parts of the legs, with one exception, were isometric to their own total leg length. The body of S. invicta Abbreviation: / HL: head length BL: body length HW1: width across the eyes HW2: width above the eyes HW3: width below the eye

Fecundity and the Body Length of Rag Worm, Perinereis Cultrifera (Grube 1840) From Wearlilir Beach Waters, Small Kei Islands, Southeast Maluku District

The knowledge of fecundity is an important aspect in the reproductive biology. Understanding the fecundity may allow the estimation of the number of rag worm individual and the determination of the number of rag worm in the questioned length class. The number of egg released represents a linking chain for one generation to next generation. The objective of research is to understand the range of fecundity, the range of body length, and the relationship of fecundity and body length of rag worm from Wearlilir waters, Moluccas, Indonesia. Achieving this objective, the observation to 238 individuals of female rag worm which are captured at Wearlilir beach waters, Small Kei Islands, Southeast Maluku District for a year from June 2010 to May 2011. The fecundity is calculated with the mixed methods including volumetric, gravimetric, and arithmetic. The relationship between fecundity and body length of rag worm is following the square function, F = 144.6533PT1.2911. It can be transformed into a form of natural logarithm to produce the regression equation: ln (WF) = 4.97434 + 1.29109 * ln (WP). Result of linear regression analysis of variance indicates that there is a positive relationship between the fecundity and body length. This relationship is not so close because only 26 % fecundities are influenced by the length, while 74 % are influenced by other factors such as environment and food

Universality in few-body systems with large scattering length

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with short-range interactions and large two-body scattering length. Such systems display remarkable universal features. In systems with more than two particles, a three-body force with limit cycle behavior is required for consistent renormalization already at leading order. We will review this EFT and some of its applications in the physics of cold atoms and nuclear physics. In particular, we will discuss the possibility of an infrared limit cycle in QCD. Recent extensions of the EFT approach to the four-body system and N-boson droplets in two spatial dimensions will also be addressed.Comment: 11 pages, 10 ps figures, invited talk at the workshop on "Nuclei and Mesoscopic Physics", Michigan State University, October 200

Three particles in an external trap: Nature of the complete J=0 spectrum

Three bosonic, spin-polarized atoms in a spherical oscillator potential constitutes the simplest nontrivial Bose-Einstein condensate (BEC). The present paper develops the tools needed to understand the nature of the complete J=0 energy spectrum for this prototype system, assuming a sum of two-body potentials. The resulting spectrum is calculated as a function of the two-body scattering length a_sc, which documents the evolution of certain many-body levels that evolve from BEC-type to molecular-type as the scattering length is decreased. Implications for the behavior of the condensate excited-state spectrum and for condensate formation and decay are elucidated. The energy levels evolve smoothly, even through the regime where the number of two-body bound states N_b increases by 1, and a_{sc} switches from -infinity to infinity. We point out the possibility of suppressing three-body recombination by tuning the two-body scattering length to values that are larger than the size of the condensate ground state. Comparisons with mean-field treatments are presented

Universal Equation for Efimov States

Efimov states are a sequence of shallow 3-body bound states that arise when the 2-body scattering length is large. Efimov showed that the binding energies of these states can be calculated in terms of the scattering length and a 3-body parameter by solving a transcendental equation involving a universal function of one variable. We calculate this universal function using effective field theory and use it to describe the three-body system of 4He atoms. We also extend Efimov's theory to include the effects of deep 2-body bound states, which give widths to the Efimov states.Comment: 8 pages, revtex4, 2 ps figures, table with numerical values of universal function adde

Universal Properties of the Four-Body System with Large Scattering Length

Few-body systems with large scattering length have universal properties that do not depend on the details of their interactions at short distances. We study the universal bound state properties of the four-boson system with large scattering length in an effective quantum mechanics approach. We compute the four-body binding energies using the Yakubovsky equations for positive and negative scattering length. Moreover, we study the correlation between three- and four-body energies and present a generalized Efimov plot for the four-body system. These results are useful for understanding the cluster structure of nuclei and for the creation of weakly-bound tetramers with cold atoms close to a Feshbach resonance.Comment: 14 pages, 4 ps figures, minor changes, version to appear in EPJ

Three-boson problem near a narrow Feshbach resonance

We consider a three-boson system with resonant binary interactions and show that three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.Comment: published versio

Many-body localization and quantum ergodicity in disordered long-range Ising models

Ergodicity in quantum many-body systems is - despite its fundamental importance - still an open problem. Many-body localization provides a general framework for quantum ergodicity, and may therefore offer important insights. However, the characterization of many-body localization through simple observables is a difficult task. In this article, we introduce a measure for distances in Hilbert space for spin-1/2 systems that can be interpreted as a generalization of the Anderson localization length to the many-body Hilbert space. We show that this many-body localization length is equivalent to a simple local observable in real space, which can be measured in experiments of superconducting qubits, polar molecules, Rydberg atoms, and trapped ions. Using the many-body localization length and a necessary criterion for ergodicity that it provides, we study many-body localization and quantum ergodicity in power-law-interacting Ising models subject to disorder in the transverse field. Based on the nonequilibrium dynamical renormalization group, numerically exact diagonalization, and an analysis of the statistics of resonances we find a many-body localized phase at infinite temperature for small power-law exponents. Within the applicability of these methods, we find no indications of a delocalization transition.Comment: 11 pages, 2 figures, extended version, added reference