Derivation of the Effective Dynamics for the Bose Polaron

Abstract

In this doctoral thesis, we consider the dynamics of a dense quantum gas consisting of $N$ bosons evolving in $\mathbb{R}^3$ in the presence of an impurity particle in the mean-field scaling with initially high density $\rho$ and large volume $\Lambda$ of the gas. In the initial state of the system almost all bosons are in the Bose-Einstein condensate, with a few excitations. For this system we derive from the microscopic dynamics in the limit of large densities and volumes the effective description by a quantum field theory modelled by the Bogoliubov-Fröhlich Hamiltonian which describes a quasi-particle, the Bose polaron.