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We exactly calculate the full temperature dependence of Casimir-like forces appearing between two and three static impurities loaded in the ideal Bose gas below the Bose–Einstein condensation transition point. Assuming the short-ranged character of the boson-impurity interaction, the calculation procedure presented here can be easily extended on a Bose system with an arbitrary number of impurities immersed.

Two- and three-body effective potentials between impurities in ideal BEC