Small system, large scattering length

The results for $a_{3D}/a_\perp =1$ are shown in Figs. 3.5-3.6. In this case the HS and SS potential give significantly different results in the large $\lambda$ regime. For both potentials the mean-field description is inadequate. By decreasing $\lambda$ the HS system enters the Tonks-Girardeau regime before approaching the LL results, whereas the SS system crosses from the ideal gas (IG) regime to the Tonks-Girardeau regime. For this value of $a_{3D}/a_\perp$ the DMC results with the Hamiltonian (3.8) coincide exactly with the ones of the LL equation of state in LDA due to the large coupling constant.

Figure 3.5: Energy per particle 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.

Figure 3.6: 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.