Resolving the puzzle of sound propagation in a dilute Bose-Einstein condensate

A unified model of a dilute Bose-Einstein condensate is proposed, combining of the logarithmic and Gross-Pitaevskii nonlinear terms in a wave equation, where the Gross-Pitaevskii term describes two-body interactions, as suggested by standard perturbation theory; while the logarithmic term is essentially non-perturbative, and takes into account quantum vacuum effects. The model is shown to have excellent agreement with sound propagation data in the condensate of cold sodium atoms known since the now classic works by Andrews and collaborators. The data also allowed us to place constraints on two of the unified model's parameters, which describe the strengths of the logarithmic and Gross-Pitaevskii terms. Additionally, we suggest an experiment constraining the value of the third parameter (the characteristic density scale of the logarithmic part of the model), using the conjectured attraction-repulsion transition of many-body interaction inside the condensate.