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Volumn 57, Issue 2, 1998, Pages 1230-1247

Microscopic treatment of binary interactions in the nonequilibrium dynamics of partially Bose-condensed trapped gases

Author keywords

[No Author keywords available]

Indexed keywords

CONDENSATION; ELECTRONIC DENSITY OF STATES; EQUATIONS OF MOTION; GASES; NONLINEAR EQUATIONS; PHASE DIAGRAMS; TEMPERATURE;

EID: 0031998223     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.1230     Document Type: Article
Times cited : (117)

References (59)
  • 23
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    • When referring to weak interactions in this paper, we mean that the effect of the medium on a typical (repeated) binary collision is not large enough to cause appreciable modification of the effective interaction from the two-body (Formula presented) matrix (Formula presented). This is indeed true if (Formula presented), where (Formula presented) is the atomic density and (Formula presented) the trap level spacing
    • When referring to weak interactions in this paper, we mean that the effect of the medium on a typical (repeated) binary collision is not large enough to cause appreciable modification of the effective interaction from the two-body (Formula presented) matrix (Formula presented). This is indeed true if (Formula presented), where (Formula presented) is the atomic density and (Formula presented) the trap level spacing.
  • 24
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    • SPHJAR
    • S. T. Beliaev, Zh. Éksp. Teor. Fiz. 34, 433 (1958) [Sov. Phys. JETP 7, 299 (1958)].SPHJAR
    • (1958) Sov. Phys. JETP , vol.7 , pp. 299
    • Beliaev, S.T.1
  • 29
    • 85037202008 scopus 로고    scopus 로고
    • H. Shi, Ph.D. thesis, University of Toronto (1997)
    • H. Shi, Ph.D. thesis, University of Toronto (1997).
  • 32
    • 85037251591 scopus 로고    scopus 로고
    • An alternative approach using Green’s functions has been independently carried out by Griffin
    • An alternative approach using Green’s functions has been independently carried out by Griffin 24. In Griffin’s approach, however, the HFB equations are considered in the limit of (Formula presented)-function pseudopotentials, as will be discussed in more detail in Sec. V.
  • 39
    • 85037241732 scopus 로고
    • Cambridge University Press, Cambridge, MA
    • F. Lalöe, in Bose-Einstein Condensation, edited by A. Griffin, D. W. Snoke and S. Stringari (Cambridge University Press, Cambridge, MA, 1995).
    • (1995)
    • Lalöe, F.1    Condensation, B.-E.2
  • 40
    • 85037249164 scopus 로고    scopus 로고
    • Philos. Trans. R. Soc. London, Ser. A (to be published)
    • N. P. Proukakis and K. Burnett, Philos. Trans. R. Soc. London, Ser. A (to be published).
    • Proukakis, N.P.1    Burnett, K.2
  • 41
    • 85037230641 scopus 로고    scopus 로고
    • We point out that this distinction between the matrix elements (Formula presented) and (Formula presented) was not explicitly analyzed in
    • We point out that this distinction between the matrix elements (Formula presented) and (Formula presented) was not explicitly analyzed in 22, although all equations of motion appearing there [i.e., all equations after (17) in 22] made use of this symmetrized matrix element of the interaction potential. We note that the use of the symmetrized matrix element greatly simplifies all subsequent expressions, and has therefore also been adopted in this paper.
  • 46
    • 0003527974 scopus 로고
    • John Wiley and Sons, New York
    • K. Huang, Statistical Mechanics, 2nd ed. (John Wiley and Sons, New York, 1987).
    • (1987) Statistical Mechanics
    • Huang, K.1
  • 48
    • 85037223306 scopus 로고    scopus 로고
    • N. P. Proukakis, D. Phil. thesis, University of Oxford (1997)
    • N. P. Proukakis, D. Phil. thesis, University of Oxford (1997).
  • 50
    • 85037224799 scopus 로고    scopus 로고
    • Here we are assuming that the anomalous correlation (Formula presented) acquires no equilibrium value in the assembly, just as was done in Sec. II for (Formula presented)
    • Here we are assuming that the anomalous correlation (Formula presented) acquires no equilibrium value in the assembly, just as was done in Sec. II for (Formula presented)
  • 52
    • 0031124645 scopus 로고    scopus 로고
    • PLRAAN
    • We would like to point out that kinetic processes have also been discussed in C. W. Gardiner and P. Zoller, Phys. Rev. A 55, 2902 (1997).PLRAAN
    • (1997) Phys. Rev. A , vol.55 , pp. 2902
    • Gardiner, C.W.1    Zoller, P.2
  • 53
    • 85037248691 scopus 로고    scopus 로고
    • This was first suggested to us in terms of our formalism by Ignacio Cirac
    • This was first suggested to us in terms of our formalism by Ignacio Cirac.
  • 54
    • 85037200131 scopus 로고    scopus 로고
    • At this point, we note that we are interested in the evolution of the condensate mean field. If we were dealing with dressing on the evolution of excited bare particle states, for example, we would also need to consider a split (Formula presented); a fully self-consistent approach would further necessitate (Formula presented) [implying that we no longer need to assume that (Formula presented) as (Formula presented)], as well as (Formula presented) and (Formula presented). We hope to return to this exact linearization procedure in a future publication dealing with the damping of quasiparticles
    • At this point, we note that we are interested in the evolution of the condensate mean field. If we were dealing with dressing on the evolution of excited bare particle states, for example, we would also need to consider a split (Formula presented); a fully self-consistent approach would further necessitate (Formula presented) [implying that we no longer need to assume that (Formula presented) as (Formula presented)], as well as (Formula presented) and (Formula presented). We hope to return to this exact linearization procedure in a future publication dealing with the damping of quasiparticles.


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