Scattering theory and equation of state of a spherical two-dimensional Bose gas

TL;DR

This paper develops a scattering theory for a spherical 2D Bose gas, deriving its equation of state and superfluid density, with implications for microgravity experiments on bubble-trapped Bose-Einstein condensates.

Contribution

It provides a novel scattering framework and equation of state for spherical 2D Bose gases, including finite-radius corrections and a microscopic derivation of superfluid density.

Findings

Derived the contact interaction strength in terms of s-wave scattering length.

Regularized the zero-point energy and obtained the equation of state with finite-radius corrections.

Reproduced the superfluid density result previously postulated.

Abstract

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 coincides with the flat-case result in the infinite-radius limit. We also provide a microscopic derivation of the superfluid density of the system, reproducing a result postulated in a previous work. Our results are relevant for modeling the ongoing microgravity experiments with two-dimensional bubble-trapped Bose-Einstein condensates.