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Small system, small scattering length

In Figs. 3.3-3.4 we present results for $a_{3D}/a_\perp =0.04$, corresponding to a less tight transverse confinement or, equivalently, to a smaller scattering length. By decreasing $a_{3D}/a_\perp $ we enter more deeply in the universal regime where the theory of pseudo-potentials applies and we find no difference between HS and SS results. Further, as for the $a_{3D}/a_\perp =0.2$ case, we find no difference between DMC results obtained starting from Hamiltonian (3.1) and from the 1D Hamiltonian (3.8). Compared to Figs. 3.1-3.2, the cross-over between mean field and Lieb-Liniger occurs for smaller values of $\lambda $. For the smallest values of $\lambda $ beyond mean-field effects become evident, though one would need to decrease $\lambda $ even further to enter the Tonks-Girardeau gas regime.

Figure 3.3: Energy per particle as a function of $\lambda $. DMC results: HS potential (solid circles), LL Hamiltonian (3.8) (open triangles), Dashed line: GP equation (3.3), solid line: LL equation of states in LDA, dotted line: TG gas, dot-dashed line: non-interacting gas.

Figure 3.4: Mean square radius along $z$ as a function of $\lambda $. Dashed line: GP equation (3.3), solid line: LL equation of states in LDA, dotted line: TG gas, dot-dashed line: non-interacting gas.


next up previous contents
Next: Small system, large scattering Up: Results Previous: Small system, medium scattering   Contents
G.E. Astrakharchik 15-th of December 2004