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We examine ground state correlations for repulsive, quasi one-dimensionalbosons in a harmonic trap. In particular, we focus on the few particle limitN=2,3,4,..., where exact numerical solutions of the many particle Schroedingerequation are available employing the Multi-Configuration Time-dependent Hartreemethod. Our numerical results for the inhomogeneous system are modeled with theanalytical solution of the homogeneous problem using the Bethe ansatz and thelocal density approximation. Tuning the interaction strength from the weaklycorrelated Gross-Pitaevskii- to the strongly correlated Tonks-Girardeau regimereveals finite particle number effects in the second order correlation functionbeyond the local density approximation.

The granularity of weakly occupied bosonic fields beyond the local density approximation