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

Abstract

We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in ${\mathbb{R}}^3$. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to $\frac{1}{N}$ 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 $N\to \infty$. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials.

AMS Latex, 29 pages

References in corpus (3)

• On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
• On the uniqueness of solutions to the Gross-Pitaevskii hierarchy
• Emission of Cherenkov Radiation as a Mechanism for Hamiltonian Friction