Energy-dependent scattering and the Gross-Pitaevskii equation in two-dimensional Bose-Einstein condensates

Lee, M. D., Morgan, S. A., Davis, M. J. and Burnett, K. (2002) Energy-dependent scattering and the Gross-Pitaevskii equation in two-dimensional Bose-Einstein condensates. Physical Review A, 65 4: 043617-1-043617-10. doi:10.1103/PhysRevA.65.043617

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Author Lee, M. D.
Morgan, S. A.
Davis, M. J.
Burnett, K.
Title Energy-dependent scattering and the Gross-Pitaevskii equation in two-dimensional Bose-Einstein condensates
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
1094-1622
Publication date 2002-04-01
Year available 2002
Sub-type Article (original research)
DOI 10.1103/PhysRevA.65.043617
Open Access Status File (Publisher version)
Volume 65
Issue 4
Start page 043617-1
End page 043617-10
Total pages 10
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Abstract We consider many-body effects on particle scattering in one-, two-, and three-dimensional (3D) Bose gases. We show that at T=0 these effects can be modeled by the simpler two-body T matrix evaluated off the energy shell. This is important in 1D and 2D because the two-body T matrix vanishes at zero energy and so mean-field effects on particle energies must be taken into account to obtain a self-consistent treatment of low-energy collisions. Using the off-shell two-body T matrix we obtain the energy and density dependence of the effective interaction in 1D and 2D and the appropriate Gross-Pitaevskii equations for these dimensions. Our results provide an alternative derivation of those of Kolomeisky and co-workers. We present numerical solutions of the Gross-Pitaevskii equation for a 2D condensate of hard-sphere bosons in a trap. We find that the interaction strength is much greater in 2D than for a 3D gas with the same hard-sphere radius. The Thomas-Fermi regime is, therefore, approached at lower condensate populations and the energy required to create vortices is lowered compared to the 3D case.
Keyword Optics
Physics, Atomic, Molecular & Chemical
2 Dimensions
Wave-guide
Gas
Systems
Bosons
Atoms
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Physical Sciences Publications
 
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Created: Thu, 20 Sep 2007, 01:50:29 EST