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Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.3/62786
- Numerical method for evolving the dipolar projected Gross-Pitaevskii equation
- Blakie, P. B.; Ticknor, C.; Bradley, A. S.; Martin, A. M.; Davis, M. J.; Kawaguchi, Y.
- We describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for an interacting Bose gas in a harmonic-oscillator potential, with the inclusion of a long-range dipolar interaction. The central difficulty in solving this equation is the requirement that the field is restricted to a small set of prescribed modes that constitute the low-energy c-field region of the system. We present a scheme, using a Hermite-polynomial-based spectral representation, which precisely implements this mode restriction and allows an efficient and accurate solution of the dipolar PGPE. We introduce a set of auxiliary oscillator states to perform a Fourier transform necessary to evaluate the dipolar interaction in reciprocal space. We extensively characterize the accuracy of our approach and derive Ehrenfest equations for the evolution of the angular momentum.
- Publication type
- Journal article
- Research centre
- Swinburne University of Technology. Faculty of Engineering and Industrial Sciences. Centre for Atom Optics and Ultrafast Spectroscopy
- Physical Review E, Vol. 80, no. 1 (Jul 2009)
- Publication year
- FOR Code(s)
- 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics; 0203 Classical Physics
- Bose gases; Dipolar interactions; Einstein condensation dynamics; Gross-Pitaevskii equation
- American Physical Society
- Publisher URL
- Copyright © 2009 The American Physical Society.
- Peer reviewed