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10
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4444285352
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C. J. Myatt, E. A. Burt, R. W. Ghrist, E. A. Cornell, and C. E. Wieman, Phys. Rev. Lett. 78, 586 (1997).
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Myatt, C.J.1
Burt, E.A.2
Ghrist, R.W.3
Cornell, E.A.4
Wieman, C.E.5
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13
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85037200564
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Throughout this paper, harmonic oscillator units (h.o.u.) are used, where for atoms of mass m trapped in a harmonic trap of frequency (Formula presented) the units of length, time, and energy are (Formula presented) (Formula presented) and (Formula presented) respectively. As a result of this scaling, the wave function is redefined so that the total density (Formula presented) is normalized to unity, and (Formula presented) where N is the total number of atoms per unit length along the z axis. We define (Formula presented) and (Formula presented) where the scattering lengths between atoms in the same hyperfine level are denoted by (Formula presented) and (Formula presented) while (Formula presented) represents scattering between hyperfine states
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Throughout this paper, harmonic oscillator units (h.o.u.) are used, where for atoms of mass m trapped in a harmonic trap of frequency (Formula presented) the units of length, time, and energy are (Formula presented) (Formula presented) and (Formula presented) respectively. As a result of this scaling, the wave function is redefined so that the total density (Formula presented) is normalized to unity, and (Formula presented) where N is the total number of atoms per unit length along the z axis. We define (Formula presented) and (Formula presented) where the scattering lengths between atoms in the same hyperfine level are denoted by (Formula presented) and (Formula presented) while (Formula presented) represents scattering between hyperfine states.
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14
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85037212629
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We used a fast Fourier transform method, where a 2D wave function is typically discretized on a (Formula presented) grid inside a (Formula presented) box, while for 3D we employed a (Formula presented) grid. The time step (Formula presented) must be small enough to ensure stability over sufficiently long propagation times; (Formula presented) is adequate for most purposes
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We used a fast Fourier transform method, where a 2D wave function is typically discretized on a (Formula presented) grid inside a (Formula presented) box, while for 3D we employed a (Formula presented) grid. The time step (Formula presented) must be small enough to ensure stability over sufficiently long propagation times; (Formula presented) is adequate for most purposes.
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15
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0000781489
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D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, Phys. Rev. Lett. 81, 1539 (1998).
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Hall, D.S.1
Matthews, M.R.2
Ensher, J.R.3
Wieman, C.E.4
Cornell, E.A.5
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16
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85037211020
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Parameters in our simulations are chosen to reflect closely those in the experiment
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Parameters in our simulations are chosen to reflect closely those in the experiment 13. In particular, (Formula presented) (Formula presented) (Formula presented) and (Formula presented) Ratios of the scattering lengths are taken to be (Formula presented) and (Formula presented) where (Formula presented)
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20
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17344369197
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Phys. Rev. AS. A. Morgan et al, 57, 3818 (1998).
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Morgan, S.A.1
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22
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85037242348
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To compare simulated lifetimes to physical results, we excite modes in a single condensate and propagate in complex time. Using this procedure, we estimate that a damping rate of (Formula presented) corresponds to typical experimental values
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To compare simulated lifetimes to physical results, we excite modes in a single condensate and propagate in complex time. Using this procedure, we estimate that a damping rate of (Formula presented) corresponds to typical experimental values
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24
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4243065368
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However, we present results for (Formula presented) to clearly illustrate the physical effect of Landau damping
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Phys. Rev. Lett.D. S. Jin et al, 78, 764 (1997).However, we present results for (Formula presented) to clearly illustrate the physical effect of Landau damping.
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Jin, D.S.1
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29
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0001241957
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A. Sinatra, P. O. Fedichev, Y. Castin, J. Dalibard, and G. V. Shlyapnikov, Phys. Rev. Lett. 82, 251 (1999).
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Sinatra, A.1
Fedichev, P.O.2
Castin, Y.3
Dalibard, J.4
Shlyapnikov, G.V.5
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31
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85037227421
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Due to the anisotropy of the trap, the dipole mode corresponding to oscillations along the “slow” x axis possesses a lower energy than along y. Displacement of the trap initially leads to oscillations along the “fast” axis as previously; however, the broken symmetry now results in transitions that gradually populate the lower level
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Due to the anisotropy of the trap, the dipole mode corresponding to oscillations along the “slow” x axis possesses a lower energy than along y. Displacement of the trap initially leads to oscillations along the “fast” axis as previously; however, the broken symmetry now results in transitions that gradually populate the lower level.
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32
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0000214462
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B. D. Esry, C. H. Greene, J. P. Burke, and J. L. Bohn, Phys. Rev. Lett. 78, 3594 (1997).
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Esry, B.D.1
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34
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0000360343
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Phys. Rev. Lett.H. Pu and N. P. Bigelow, 80, 1130 (1998).
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Pu, H.1
Bigelow, N.P.2
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