Two-fluid hydrodynamics for a trapped weakly interacting Bose gas

Zaremba, E.; Griffin, Allan; Nikuni, Tetsuro

doi:10.1103/physreva.57.4695

Cited by 95 publications

(136 citation statements)

References 13 publications

(26 reference statements)

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“…Particularly motivated by the desire to explain the properties of Bose-condensed gases at finite temperature, a number of extensions have been proposed. These include generalizations [58,59,60,61,62,63,64] of linear response theory [65,66], stochastic interpretations of the Gross-Pitaevskii equation [67,68,69,70,71], Hartree-Fock-Bogoliubov approaches [72,73,74,75,76,77,78], a variety of kinetic theories [79,80,81,82,83,84,85,86,87,88,89,90], and a cumulant-based formalism [21,91,92,93].…”

Section: Introductionmentioning

confidence: 99%

Number-conserving approach to a minimal self-consistent treatment of condensate and noncondensate dynamics in a degenerate Bose gas

Gardiner

Morgan

2007

Phys. Rev. A

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. (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 . p. 43621.Further information on publisher's website: Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 3008 (1998)]. We consider what is effectively an expansion in powers of the ratio of non-condensate 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 non-condensate 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 numberconserving 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 at occurring at finite temperature, where there is a significant non-condensate fraction from the outset, or dynamics leading to dynamical instabilities, where depletion of the condensate can also lead to a significant non-condensate fraction, even if the non-condensate fraction is initially negligible.

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Section: Introductionmentioning

confidence: 99%

Number-conserving approach to a minimal self-consistent treatment of condensate and noncondensate dynamics in a degenerate Bose gas

Gardiner

Morgan

2007

Phys. Rev. A

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“…These equations govern in a self-consistent way the dynamics of the condensate, the thermal cloud and the anomalous average. Our time dependent HartreeFock-Bogoliubov (TDHFB) equations generalize in a natural way many of the famous approximations found in the literature such as the Bogoliubov, the Gross-Pitaevskii [67,68], the Popov [69], the Beliaev [70], the Bogoliubov-de Gennes [36] ZNG equations [22] and others.…”

Section: Discussionmentioning

confidence: 99%

Anomalous density for Bose gases at finite temperature

Boudjemâa¹,

Benarous²

2011

Phys. Rev. A

102

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We analyze the behavior of the anomalous density as function of the radial distance at different temperatures in a variational framework. We show that the temperature dependence of the anomalous density agrees with the Hartree-Fock-Bogoliubov (HFB) calculations. Comparisons between the normal and the anomalous fractions at low temperature show that the latter remains higher and consequently the neglect of the anomalous density may destabilize the condensate. These results are compatible with those of Yukalov. Surprisingly, the study of the anomalous density in terms of the interaction parameter shows that the dip in the central density is destroyed for sufficiently weak interactions. We explain this effect.

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“…There are, of course alternative approaches to the general issue of combining kinetic theory and quantum mechanics, which have different emphases. For example Stoof [21] has chosen to develop an approach which avoids the use of the pseudopotential method, which he has shown will fail very near the critical point; Walser et al [22] have developed a kinetic approach somewaht more related to ours; while Zaremba et al [23] have developed a two fluid hydrodynamic description. The major criterion for choosing a particular approach will ultimately be the degree of usefulness in explaining experiments, and its ease of use-but we will leave this judgment on this to the BEC community.…”

Section: Introductionmentioning

confidence: 99%