A Galërkin projection and multiple scales approach to Feshbach resonance in Bose–Einstein condensates

Karl H. Frinkle

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 74, issue 2, 126-134

Abstract: In this paper, solutions of the nonlinear Schrödinger equation with a parabolic and a periodic potential modelling the dynamics of Bose–Einstein condensates are considered. A Galërkin projection approach is applied to reduce the partial differential equation to a system of nonlinear ordinary differential equations. In the case of Feshbach resonance, a multiple scales approach is applied to the reduced equations and is used to capture the dynamics of the full behavior of the PDE. Averaging is also used when the period of the oscillations corresponds to that of the difference in eigenvalues, thus inducing a resonance in the reduced equations. Accurate predictions of the overall behavior of the PDE can be made through this simplified model, including some very interesting resonance results.

Keywords: Bose–Einstein condensates; Feshbach resonance; Galërkin projections (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:74:y:2007:i:2:p:126-134

DOI: 10.1016/j.matcom.2006.10.015

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