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A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas

Gardiner, S.A.; Morgan, S.A.

Authors

S.A. Morgan



Abstract

We describe a number-conserving approach to the dynamics of Bose-Einstein condensed dilute atomic gases. This builds upon the works of Gardiner [Phys. Rev. A 56, 1414 (1997)] and Castin and Dum [Phys. Rev. A 57, 3008 (1998)]. We consider what is effectively an expansion in powers of the ratio of noncondensate to condensate particle numbers, rather than inverse powers of the total number of particles. This requires the number of condensate particles to be a majority, but not necessarily almost equal to the total number of particles in the system. We argue that a second-order treatment of the relevant dynamical equations of motion is the minimum order necessary to provide consistent coupled condensate and noncondensate number dynamics for a finite total number of particles, and show that such a second-order treatment is provided by a suitably generalized Gross-Pitaevskii equation, coupled to the Castin-Dum number-conserving formulation of the Bogoliubov–de Gennes equations. The necessary equations of motion can be generated from an approximate third-order Hamiltonian, which effectively reduces to second order in the steady state. Such a treatment as described here is suitable for dynamics occurring at finite temperature, where there is a significant noncondensate fraction from the outset, or dynamics leading to dynamical instabilities, where depletion of the condensate can also lead to a significant noncondensate fraction, even if the noncondensate fraction is initially negligible.

Citation

Gardiner, S., & Morgan, S. (2007). A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas. Physical Review A, 75, https://doi.org/10.1103/physreva.75.043621

Journal Article Type Article
Publication Date Apr 1, 2007
Deposit Date Apr 28, 2008
Publicly Available Date Apr 28, 2008
Journal Physical Review A
Print ISSN 1050-2947
Electronic ISSN 1094-1622
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 75
DOI https://doi.org/10.1103/physreva.75.043621
Public URL https://durham-repository.worktribe.com/output/1549394

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