In Ref. 11 clustering representations of the position distribution of the ideal Bose gas were considered. In principle that gives rise to possibilities concerning simulations of the system of positions of the particles. But one has to take into account that in case of low temperature the clusters are very large and their origins are far from a fixed bounded volume. For that reason we will consider some estimations of the influence of these clusters on the behavior of the subsystem of particles located in a fixed bounded volume. All points in the fixed bounded volume come from a bigger volume which the estimation (5.2) in Theorem 5.2 gives on average. Several numerical simulations in dimension two are shown in Sec. 5.
Casimir forces for the ideal Bose gas in anisotropic optical lattices: the effect of alternating sign upon varying dimensionality