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Quantum fluctuations will give a finite density at the nodal surfaces, so that a more correct statement would refer to a "nearly vanishing density."
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The existence of nodal BEC solutions with j nodes at well depths shallower than that necessary for the existence of the noninteracting single particle bound state with j nodes is due to the presence of the BEC chemical potential creating an effectively deeper well.
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The existence of nodal BEC solutions with j nodes at well depths shallower than that necessary for the existence of the noninteracting single particle bound state with j nodes is due to the presence of the BEC chemical potential creating an effectively deeper well.
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77953186473
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The reason that ΔF>0 for well depths near those where the nodal solutions first exist is related to the appearance of the nodal BEC solutions at well depths shallower than that for the corresponding noninteracting bound states, cf. [21].
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The reason that Δ F > 0 for well depths near those where the nodal solutions first exist is related to the appearance of the nodal BEC solutions at well depths shallower than that for the corresponding noninteracting bound states, cf. [21].
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A thorough analysis of the diagonalization of the L operator is given by, in edited by R. Kaiser, C. Westbrook, and F. David (Springer-Verlag, Berlin
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A thorough analysis of the diagonalization of the L operator is given by Y. Castin, in Coherent Atomic Matter Waves, Lecture Notes of the Les Houches Summer School, edited by, R. Kaiser,,, C. Westbrook,, and, F. David, (Springer-Verlag, Berlin, 2001); and
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e-print arXiv: cond-mat/0105058
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e-print arXiv: cond-mat/0105058.
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26
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77953227771
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The L operator is actually not quite diagonalizable, as discussed in [24]. This problem can be remedied by introducing a projection operator that projects out the overlap of δ with o. However, the modified L operator has the same spectrum as the L operator, so the conclusions remain unaltered.
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The L operator is actually not quite diagonalizable, as discussed in [24]. This problem can be remedied by introducing a projection operator that projects out the overlap of δ with o. However, the modified L operator has the same spectrum as the L operator, so the conclusions remain unaltered.
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Vm- goes to 0 for large distances and Vm+ goes to 2 since o2→1; thus the Vm- energy level passing through 0 corresponds to an unbinding transition while for Vm+ it does not.
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V m - goes to 0 for large distances and V m + goes to 2 since o 2 → 1; thus the V m - energy level passing through 0 corresponds to an unbinding transition while for V m + it does not.
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