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

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

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

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

Satellite potentials for hypergeometric Natanzon potentials

As a result of the so(2,1) of the hypergeometric Natanzon potential a set of potentials related to the given one is determined. The set arises as a result of the action of the so(2,1) generators.Comment: 9 page

‘Question Moments’: A Rolling Programme of Question Opportunities in Classroom Science

This article has been made available through the Brunel Open Access Publishing Fund.This naturalistic study integrates specific 'question moments' into lesson plans to increase pupils' classroom interactions. A range of teaching tools has explored students' ideas through opportunities to ask and write questions. Their oral and written outcomes provide data on individual and group misunderstandings. Changes to the schedule of lessons were introduced to discuss these questions and solve disparities. Flexible lesson planning over fourteen lessons across a four-week period of highschool chemistry accommodated students' contributions and increased student participation, promoted inquiring and individualised teaching, with each teaching strategy feeding forward into the next

New Shape Invariant Potentials in Supersymmetric Quantum Mechanics

Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for energy eigenvalues, eigenfunctions and transmission coefficients are given. Included in our potentials as a special case is the self-similar potential recently discussed by Shabat and Spiridonov.Comment: 8pages, Te