Mean field dynamics of a quantum tracer particle interacting with a boson gas

We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in R-3. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to 1/N, where N is the expected particle number. Assuming that the mass of the tracer particle is proportional to N, we derive generalized Hartree equations in the limit N -> infinity. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials. (C) 2018 Elsevier Inc. All rights reserved.