The Renormalised Bogoliubov-Fr\"ohlich Hamiltonian

Abstract

The Bogoliubov-Fr\"ohlich Hamiltonian models the interaction of an impurity with the excitations of a Bose-Einstein condensate. It has been observed that the dependence of the ground state energy on the ultraviolet cutoff differs significantly from what would be expected from similar well-known models. We give a detailed explanation of this UV behaviour, and provide an explicit representation of the renormalised Hamiltonian.