In Figs. 3.3-3.4 we present results for
,
corresponding to a less tight transverse confinement or, equivalently, to a smaller
scattering length. By decreasing
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
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
. For the smallest values of
beyond mean-field effects become
evident, though one would need to decrease
even further to enter the
Tonks-Girardeau gas regime.
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