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Excited states in the Thomas–Fermi limit: a variational approach
Mathematics and Statistics Department Faculty Publication Series
  • M Cole
  • D E Pelinovsky
  • PG Kevrekidis, University of Massachusetts - Amherst
Publication Date
2009
Comments
This is the pre-published version harvested from arXiv.
Abstract

Excited states of Bose–Einstein condensates are considered in the semi-classical (Thomas- Fermi) limit of the Gross–Pitaevskii equation with repulsive inter-atomic interactions and a harmonic potential. The relative dynamics of dark solitons (density dips on the localized condensate) with respect to the harmonic potential and to each other is approximated using the averaged Lagrangian method. This permits a complete characterization of the equilibrium positions of the dark solitons as a function of the chemical potential parameter. It also yields an analytical handle on the oscillation frequencies of dark solitons around such equilibria. The asymptotic predictions are generalized for an arbitrary number of dark solitons and are corroborated by numerical computations for 2- and 3-soliton configurations

Citation Information
M Cole, D E Pelinovsky and PG Kevrekidis. "Excited states in the Thomas–Fermi limit: a variational approach" (2009)
Available at: http://works.bepress.com/panos_kevrekidis/41/