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23
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85037229027
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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
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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.
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24
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0000724476
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SPHJAR
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S. T. Beliaev, Zh. Éksp. Teor. Fiz. 34, 433 (1958) [Sov. Phys. JETP 7, 299 (1958)].SPHJAR
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Beliaev, S.T.1
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85037202008
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H. Shi, Ph.D. thesis, University of Toronto (1997)
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H. Shi, Ph.D. thesis, University of Toronto (1997).
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32
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85037251591
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An alternative approach using Green’s functions has been independently carried out by Griffin
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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.
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39
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85037241732
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Cambridge University Press, Cambridge, MA
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F. Lalöe, in Bose-Einstein Condensation, edited by A. Griffin, D. W. Snoke and S. Stringari (Cambridge University Press, Cambridge, MA, 1995).
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Lalöe, F.1
Condensation, B.-E.2
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85037249164
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Philos. Trans. R. Soc. London, Ser. A (to be published)
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N. P. Proukakis and K. Burnett, Philos. Trans. R. Soc. London, Ser. A (to be published).
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Proukakis, N.P.1
Burnett, K.2
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41
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85037230641
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We point out that this distinction between the matrix elements (Formula presented) and (Formula presented) was not explicitly analyzed in
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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.
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46
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0003527974
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John Wiley and Sons, New York
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K. Huang, Statistical Mechanics, 2nd ed. (John Wiley and Sons, New York, 1987).
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Statistical Mechanics
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Huang, K.1
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48
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85037223306
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N. P. Proukakis, D. Phil. thesis, University of Oxford (1997)
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N. P. Proukakis, D. Phil. thesis, University of Oxford (1997).
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50
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85037224799
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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)
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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)
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52
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0031124645
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PLRAAN
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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
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(1997)
Phys. Rev. A
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Gardiner, C.W.1
Zoller, P.2
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53
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85037248691
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This was first suggested to us in terms of our formalism by Ignacio Cirac
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This was first suggested to us in terms of our formalism by Ignacio Cirac.
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54
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85037200131
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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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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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58
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0000393590
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PLRAAN
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R. J. Dodd, M. Edwards, C. W. Clark, and K. Burnett, Phys. Rev. A 57, 32 (1998).PLRAAN
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(1998)
Phys. Rev. A
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Dodd, R.J.1
Edwards, M.2
Clark, C.W.3
Burnett, K.4
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