It is well-known that the number fluctuation in the grand canonical ensemble,
which is directly proportional to the compressibility, diverges for an ideal
bose gas as T -> 0. We show that this divergence is removed when the atoms
interact in one dimension through an inverse square two-body interaction. In
two dimensions, similar results are obtained using a self-consistent
Thomas-Fermi (TF) model for a repulsive zero-range interaction. Both models may
be mapped on to a system of non-interacting particles obeying the Haldane-Wu
exclusion statistics. We also calculate the number fluctuation from the ground
state of the gas in these interacting models, and compare the grand canonical
results with those obtained from the canonical ensemble.Comment: 11 pages, 1 appendix, 3 figures. Submitted to J. Phys. B: Atomic,
Molecular & Optica