ABSTRACT
Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries [elongated and/or toroidal (annular)], we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.
ABSTRACT
It has been argued that the phenomenon of hormesis should prompt us to revise current regulatory policy in order to take beneficial effects of small doses of various agents into account. I argue that three problems--the comparative smallness of hormetic effects, the fine-tuning problem, and the problem of aggregated actions--should lead us not to overemphasize the importance of hormesis for policy, and that they, if anything, points towards a non-consequentialist approach to the ethics of risk.
