Bose atoms in a trap: a variational Monte Carlo formulation for the universal behavior at the Van der Waals length scale

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We present a variational Monte Carlo (VMC) formulation for the universal equations of state at the Van der Waals length scale [B. Gao, J. Phys. B 37, L227 (2004)] for N Bose atoms in a trap. The theory illustrates both how such equations of state can be computed exactly, and the existence and the importance of long-range atom-atom correlation under strong confinement. Explicit numerical results are presented for N=3 and 5, and used to provide a quantitative understanding of the shape-dependent confinement correction that is important for few atoms under strong confinement.