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We study the motion of a heavy impurity immersed in a weakly interacting BECusing the Gross-Pitaevskii equation (GPe). We construct a perturbative solutionto the GPe in powers of impurity velocity in the case when the boson-impuritypotential is tuned to unitarity and calculate the effective mass of thepolaron. In addition, we calculate the interaction energy of two unitarypolarons which are sufficiently far apart. Our formalism also reproduces theresults for both the mass and interaction energy obtained at weakboson-impurity coupling.

Effective mass and interaction energy of heavy Bose polarons at unitarity