Effective Dynamics for the Bose Polaron in the Large-Volume Mean-Field Limit

Abstract

We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in ${\mathbb{R}}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density $\ddot{I}$ and large volume $\hat{I}›$ of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint $\hat{I}{›}^3\ll \ddot{I}$, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.

Minor corrections and improved presentation