Publication Date
2007
Journal or Book Title
PHYSICS LETTERS A
Abstract
In this work we revisit the topic of two-dimensional Bose–Einstein condensates under the influence of time-dependent magnetic confinement and time-dependent scattering length. A moment approach reduces the examination of moments of the wavefunction (in particular, of its width) to an Ermakov–Pinney (EP) ordinary differential equation (ODE). We use the well-known structure of the solutions of this nonlinear ODE to “engineer” trapping and interatomic interaction conditions that lead to condensates dispersing, breathing or even collapsing. The advantage of the approach is that it is fully tractable analytically, in excellent agreement with our numerical observations. As an aside, we also discuss how similar time-dependent EP equations may arise in the description of anisotropic scalar field cosmologies.
Pages
140-148
Volume
367
Issue
1-2
Recommended Citation
Herring, G; Kevrekidis, PG; Williams, F; Christodoulakis, T; and Frantzeskakis, DJ, "From Feshbach-resonance managed Bose-Einstein condensates to anisotropic universes: Applications of the Ermakov-Pinney equation with time-dependent nonlinearity" (2007). PHYSICS LETTERS A. 117.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/117
Comments
This is the prepublished version harvested from ArXiv. The published version is located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVM-4N56BPM-6&_user=1516330&_coverDate=07%2F16%2F2007&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=a511acd770e999877dda6f8b1987dfa8&searchtype=a