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Numerical integration of Eq.� 3 shows that the expansion [see Eq.� 5] of (Formula presented) over first-band states (Formula presented) remains valid for values of (Formula presented) as high as (Formula presented). More precisely, if at (Formula presented) the wave packet is prepared in a superposition of such states, so that (Formula presented), after a typical evolution time (Formula presented) we find (Formula presented), with (Formula presented). This shows the BEC dynamics is essentially confined to the first band, and that considering only such states is a very good approximation
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Numerical integration of Eq.� 3 shows that the expansion [see Eq.� 5] of (Formula presented) over first-band states (Formula presented) remains valid for values of (Formula presented) as high as (Formula presented). More precisely, if at (Formula presented) the wave packet is prepared in a superposition of such states, so that (Formula presented), after a typical evolution time (Formula presented) we find (Formula presented), with (Formula presented). This shows the BEC dynamics is essentially confined to the first band, and that considering only such states is a very good approximation.
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23
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85038299808
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Population transfer between wells occurs if the nonlinear frequency shift brings the energy levels of neighbor wells into degeneracy [cf.�Eq.� 14]. This condition cannot be satisfied for wells with a low population
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Population transfer between wells occurs if the nonlinear frequency shift brings the energy levels of neighbor wells into degeneracy [cf.�Eq.� 14]. This condition cannot be satisfied for wells with a low population.
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