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By considering a system uniform along the z -axis with a vertical length Z, the effective two-dimensional (2D) coupling constant is given by g2D = g3D/Z, where g3D is the 3D coupling constant. If instead the motion along z is squeezed into the lowest oscillator state, one has g2D = g3D/az 2π, where az is the axial oscillator length.
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By considering a system uniform along the z -axis with a vertical length Z, the effective two-dimensional (2D) coupling constant is given by g2D = g3D/Z, where g3D is the 3D coupling constant. If instead the motion along z is squeezed into the lowest oscillator state, one has g2D = g3D/az 2π, where az is the axial oscillator length.
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20
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84856128127
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Such description proves to be extremely useful whenever ∇·v=∇×v=0. Indeed, this implies the condition ∂ z v=0, i.e., v turns out to be an analytic function of z*. For example, for the particularly simple case of a single vortex, one has v=i/z*.
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Such description proves to be extremely useful whenever V · v=×v=0. Indeed, this implies the condition ∂ z v=0, i.e., v turns out to be an analytic function of z*. For example, for the particularly simple case of a single vortex, one has v=i/z*.
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21
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84856123886
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One has ζ(z+2j ω1 +2k ω2) =ζ(z)+2jζ (ω1) +2kζ (ω2) and ζ (ω1) ω2 -ζ (ω2) ω1 =iπ/2.
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One has ζ(z+2j ω1 +2k ω2) =ζ(z)+2jζ (ω1) +2kζ (ω2) and ζ (ω1) ω2 -ζ (ω2) ω1 =iπ/2.
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For g=0 one has μ=1, corresponding to the zero point energy of the two-dimensional harmonic trapping.
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For g=0 one has μ=1, corresponding to the zero point energy of the two-dimensional harmonic trapping.
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26
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33344474924
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The parabolic shape of the coarse grained density profile has been recently proven in the LLL regime starting from the exact solution of the GP equation.
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The parabolic shape of the coarse grained density profile has been recently proven in the LLL regime starting from the exact solution of the GP equation.
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In Ref. rv is instead defined as the mean square root radius of nmax -n on a single cell. However, such definition is not suitable for the TF regime, where it fails in reproducing the proportionality between rv and ξ.
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In Ref. rv is instead defined as the mean square root radius of nmax -n on a single cell. However, such definition is not suitable for the TF regime, where it fails in reproducing the proportionality between rv and ξ.
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