Numerical method for evolving the dipolar projected Gross-Pitaevskii equation

Blakie, P. B., Ticknor, C., Bradley, A. S., Martin, A. M., Davis, M. J. and Kawaguchi, Y. (2009) Numerical method for evolving the dipolar projected Gross-Pitaevskii equation. Physical Review E, 80 1: 016703-1-016703-16. doi:10.1103/PhysRevE.80.016703

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Author Blakie, P. B.
Ticknor, C.
Bradley, A. S.
Martin, A. M.
Davis, M. J.
Kawaguchi, Y.
Title Numerical method for evolving the dipolar projected Gross-Pitaevskii equation
Journal name Physical Review E   Check publisher's open access policy
ISSN 1539-3755
Publication date 2009-07-15
Year available 2009
Sub-type Article (original research)
DOI 10.1103/PhysRevE.80.016703
Open Access Status File (Publisher version)
Volume 80
Issue 1
Start page 016703-1
End page 016703-16
Total pages 16
Editor Gary S. Grest
Margaret Malloy
Place of publication United States
Publisher American Physical Society
Collection year 2010
Language eng
Subject C1
970102 Expanding Knowledge in the Physical Sciences
020601 Degenerate Quantum Gases and Atom Optics
Abstract 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.
Keyword Einstein Condensation Dynamics
Gas
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
 
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Created: Thu, 18 Feb 2010, 12:49:13 EST by Jessica Dalton-Morgan on behalf of Physics