Validity of the Fröhlich model for a mobile impurity in a Bose-Einstein condensate
Phys. Rev. A 112, 053319 – Published 18 November, 2025
DOI: https://doi.org/10.1103/3zd3-rxhp
Abstract
We analyze the many-body Hamiltonian describing a mobile impurity immersed in a Bose-Einstein condensate (BEC). Using exact unitary transformations and rigorous error estimates, we show the validity of the Bogoliubov-Fröhlich Hamiltonian for the Bose polaron in the regime of moderately strong, repulsive interactions with a dilute BEC. Moreover, we calculate analytically the universal logarithmic correction to the ground state energy that arises from an impurity mediated phonon-phonon interaction.
