Who is afraid of constructivism? (¿Quién tiene miedo del constructivismo?)

Both generative and constructivist researchers agree that children are able to form abstractions and produce novel grammatically patterned utterances. Both approaches are able to explain such abilities, and hence their existence does not entail an innate Universal Grammar. However, generativists and constructivists differ in their views on the nature of early generalisations: while generative researchers assume that adult-like linguistic representations are present from the very beginning, constructivists argue that children begin with relatively specific, low level schemas and gradually extract more abstract patterns. There is considerable empirical evidence for the latter position. Moreover, constructivist theories provide a better explanation for principled behaviour -not just the observed patterns, but also the absence of certain constructions in children's early productions and various developmental asynchronies. Tanto los investigadores generativistas como constructivistas coinciden en que los niños son capaces de formar abstracciones y de producir emisiones novedosas gramaticalmente estructuradas. Ambos enfoques son capaces de explicar tales habilidades, y por eso su existencia no implica una Gramática Universal innata. Sin embargo, los investigadores generativistas y constructivistas difieren en su visión sobre la naturaleza de las generalizaciones tempranas: mientras que los investigadores generativistas asumen que las representaciones lingüísticas parecidas a las adultas están presentes desde edades tempranas, los constructivistas argumentan que los niños comienzan con esquemas de bajo nivel, relativamente específicos, y que gradualmente extraen esquemas más abstractos. Existe considerable evidencia empírica en apoyo de esta segunda posición. Además, las teorías constructivistas proporcionan una mejor explicación de las conductas basadas en reglas; no sólo de los patrones observados, sino también de la ausencia de ciertas construcciones en las producciones verbales tempranas de los niños y de diversas asincronías evolutivas

Quantum depletion of collapsing Bose-Einstein condensates

We perform the first numerical three-dimensional studies of quantum field effects in the Bosenova experiment on collapsing condensates by E. Donley et al. [Nature 415, 39 (2002)] using the exact experimental geometry. In a stochastic truncated Wigner simulation of the collapse, the collapse times are larger than the experimentally measured values. We find that a finite temperature initial state leads to an increased creation rate of uncondensed atoms, but not to a reduction of the collapse time. A comparison of the time-dependent Hartree-Fock-Bogoliubov and Wigner methods for the more tractable spherical trap shows excellent agreement between the uncondensed populations. We conclude that the discrepancy between the experimental and theoretical values of the collapse time cannot be explained by Gaussian quantum fluctuations or finite temperature effects.Comment: 9 pages, 4 figures, replaced with published versio

A search on Dirac equation

The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given.Comment: 9 page

Zipf's law in Multifragmentation

We discuss the meaning of Zipf's law in nuclear multifragmentation. We remark that Zipf's law is a consequence of a power law fragment size distribution with exponent $\tau \simeq 2$. We also recall why the presence of such distribution is not a reliable signal of a liquid-gas phase transition

Ballistic deposition patterns beneath a growing KPZ interface

We consider a (1+1)-dimensional ballistic deposition process with next-nearest neighbor interaction, which belongs to the KPZ universality class, and introduce for this discrete model a variational formulation similar to that for the randomly forced continuous Burgers equation. This allows to identify the characteristic structures in the bulk of a growing aggregate ("clusters" and "crevices") with minimizers and shocks in the Burgers turbulence, and to introduce a new kind of equipped Airy process for ballistic growth. We dub it the "hairy Airy process" and investigate its statistics numerically. We also identify scaling laws that characterize the ballistic deposition patterns in the bulk: the law of "thinning" of the forest of clusters with increasing height, the law of transversal fluctuations of cluster boundaries, and the size distribution of clusters. The corresponding critical exponents are determined exactly based on the analogy with the Burgers turbulence and simple scaling considerations.Comment: 10 pages, 5 figures. Minor edits: typo corrected, added explanation of two acronyms. The text is essentially equivalent to version

Supersonic optical tunnels for Bose-Einstein condensates

We propose a method for the stabilisation of a stack of parallel vortex rings in a Bose-Einstein condensate. The method makes use of a hollow laser beam containing an optical vortex. Using realistic experimental parameters we demonstrate numerically that our method can stabilise up to 9 vortex rings. Furthermore we point out that the condensate flow through the tunnel formed by the core of the optical vortex can be made supersonic by inserting a laser-generated hump potential. We show that long-living immobile condensate solitons generated in the tunnel exhibit sonic horizons. Finally, we discuss prospects of using these solitons for analogue gravity experiments.Comment: 14 pages, 3 figures, published versio

Quantum-field dynamics of expanding and contracting Bose-Einstein condensates

We analyze the dynamics of quantum statistics in a harmonically trapped Bose-Einstein condensate, whose two-body interaction strength is controlled via a Feshbach resonance. From an initially non-interacting coherent state, the quantum field undergoes Kerr squeezing, which can be qualitatively described with a single mode model. To render the effect experimentally accessible, we propose a homodyne scheme, based on two hyperfine components, which converts the quadrature squeezing into number squeezing. The scheme is numerically demonstrated using a two-component Hartree-Fock-Bogoliubov formalism.Comment: 9 pages, 4 figure