Equation of state of a two-dimensional spherical Bose gas

We analyze the scattering problem of identical bosonic particles confined on a spherical surface. At low scattering energies, and for a radius much larger than the healing length, we express the contact interaction strength in terms of the s-wave scattering length. Adopting this relation, we are then able to regularize the zero-point energy of the spherical Bose gas and to obtain its equation of state, which includes the corrections due to the finite radius of the sphere, and that coincides with the flat-case result in the infinite-radius limit. Our results are relevant for modeling the ongoing microgravity experiments with two-dimensional bubble-trapped Bose-Einstein condensates.