Microscopic derivation of the Fr\"ohlich Hamiltonian for the Bose polaron in the mean-field limit

Abstract

We consider the quantum mechanical many-body problem of a single impurity particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the Hamiltonian of this system in the mean-field limit and rigorously show that, at low energies, the problem is well described by the Fr\"ohlich polaron model.