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- Phase space theory of Bose-Einstein condensates and time-dependent modes
- Dalton, B. J.
- A phase space theory approach for treating dynamical behaviour of Bose-Einstein condensates applicable to situations such as interferometry with BEC in time-dependent double well potentials is presented. Time-dependent mode functions are used, chosen so that one, two,...highly occupied modes describe well the physics of interacting condensate bosons in time dependent potentials at well below the transition temperature. Time dependent mode annihilation, creation operators are represented by time dependent phase variables, but time independent total field annihilation, creation operators are represented by time independent field functions. Two situations are treated, one (mode theory) is where specific mode annihilation, creation operators and their related phase variables and distribution functions are dealt with, the other (field theory) is where only field creation, annihilation operators and their related field functions and distribution functionals are involved. The field theory treatment is more suitable when large boson numbers are involved. The paper focuses on the hybrid approach, where the modes are divided up between condensate (highly occupied) modes and non-condensate (sparsely occupied) modes. It is found that there are extra terms in the Ito stochastic equations both for the stochastic phases and stochastic fields, involving coupling coefficients defined via overlap integrals between mode functions and their time derivatives. For the hybrid approach both the Fokker-Planck and functional Fokker-Planck equations differ from those derived via the correspondence rules, the drift vectors are unchanged but the diffusion matrices contain additional terms involving the coupling coefficients. Results are also presented for the combined approach where all the modes are treated as one set. Here both the Fokker-Planck and functional Fokker-Planck equations are exactly the same as those derived via the correspondence rules. However, although the Ito stochastic field equations are also unchanged, the Ito equations for the stochastic phases contain an extra classical term involving the coupling coefficients.
- Publication type
- Journal article
- Research centre
- Swinburne University of Technology. Faculty of Engineering and Industrial Sciences. Centre for Atom Optics and Ultrafast Spectroscopy
- Annals of Physics, Vol. 327, no. 10 (Oct 2012), pp. 2432-2490
- Publication year
- FOR Code(s)
- 01 Mathematical Sciences; 02 Physical Sciences
- Bose-Einstein condensates; Interferometry; Phase space theory
- Publisher URL
- Copyright © 2012 Elsevier Inc. This is the author's version of a work that was accepted for publication in Annals of Physics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Annals of Physics, [327, 10, (2012)] DOI: 10.1016/j.aop.2012.06.005.
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