Scaling limit of weakly bound triatomic states

The usefulness of a scale-independent approach to identify Efimov states in three-body systems is shown by comparing such an approach with a realistic calculation in the case of three helium atoms. We show that the scaling limit is realized in practice in this case, and suggest its application to study other similar systems, including the case where two kinds of atoms are mixed. We also consider the observed large scattering length of the Rb-87 dimer to estimate the critical value of the ground-state energy of the corresponding trimer (greater than or equal to 1.5 mK), in order to allow for one Efimov state above the ground state.

Topological signatures in CMB temperature anisotropy maps

We propose an alternative formalism to simulate cosmic microwave background (CMB) temperature maps in Lambda CDM universes with nontrivial spatial topologies. This formalism avoids the need to explicitly compute the eigenmodes of the Laplacian operator in the spatial sections. Instead, the covariance matrix of the coefficients of the spherical harmonic decomposition of the temperature anisotropies is expressed in terms of the elements of the covering group of the space. We obtain a decomposition of the correlation matrix that isolates the topological contribution to the CMB temperature anisotropies out of the simply connected contribution. A further decomposition of the topological signature of the correlation matrix for an arbitrary topology allows us to compute it in terms of correlation matrices corresponding to simpler topologies, for which closed quadrature formulas might be derived. We also use this decomposition to show that CMB temperature maps of (not too large) multiply connected universes must show patterns of alignment, and propose a method to look for these patterns, thus opening the door to the development of new methods for detecting the topology of our Universe even when the injectivity radius of space is slightly larger than the radius of the last scattering surface. We illustrate all these features with the simplest examples, those of flat homogeneous manifolds, i.e., tori, with special attention given to the cylinder, i.e., T-1 topology.

Prediction of a weakly bound excited state in the He-4(2)-Li-7 molecule

A scale-independent approach, valid for weakly bound three-body systems, is used to analyze the existence of excited Thomas-Efimov states in molecular systems with three atoms: a helium dimer together with isotopes of lithium (Li-6 and Li-7) and sodium (Na-23). With the present study and the available data, we can clearly predict that the He-4(2)-Li-7 system supports an excited state with binding energy close to 2.31 mK. (C) 2000 American Institute of Physics. [S0021-9606(00)30442-1].

Population persistence in weakly-coupled sinks

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Universality and Scaling Limit of Weakly-Bound Tetramers

The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B-3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited N-th tetramer energy B-4((N)) is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio B-4((N))/B-3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.

Matter-wave localization in a weakly perturbed optical lattice

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Finding critical exponents for two-dimensional Hamiltonian maps

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Coincidence points of fiber maps on S-n-bundles

In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.

Abelianized obstruction for fixed points of fiber-preserving maps of surface bundles

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

Development of environmental and natural vulnerability maps for Brazilian coastal at Sao Sebastiao in São Paulo State

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A PC compatible Brazilian software for obtaining thermal histories using apatite fission track analysis

In this work a software developed in the Instituto de Fisica Gleb Wataghin, IFGW, UNICAMP, Campinas, SP, Brazil for obtaining thermal histories using apatite fission track analysis is presented. This software works in Microsoft-Windows environment. It will be freely disposable in the web site of the Departamento de Raios Cosmicos, IFGW, UNICAMP. Thermal histories obtained through this software are compared with those deduced using Monte Trax the software compatible with Apple Macintosh developed by Gallagher. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Simulation of electron density maps for two-dimensional crystal structures using Mathematica

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Hausdorff dimension of non-hyperbolic repellers. I: Maps with holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.

Clarke's alpha, beta, and zero components: A possible approach for the conceptual design of instrumentation compatible with IEEE Std. 1459-2000

This paper explains the conceptual design of instrumentation that measures electric quantities defined in the Std. 1459-2000. It is shown how the instantaneous-space-phasor approach, based on alpha, beta, 0 components, can be used to monitor electric energy flow, evaluate the utilization of transmission line, and quantify the level of harmonic pollution injected by nonlinear loads.

The relationship between differential equations with piecewise constant argument and the associated discrete equations, via dichotomic maps

Dichotomic maps are considered by means of the stability and asymptotic stability of the null solution of a class of differential equations with argument [t] via associated discrete equations, where [.] designates the greatest integer function.