Derivation of the Hartree equation for compound Bose gases in the mean field limit
Ioannis Anapolitanos, Michael Hott, Dirk Hundertmark
We consider mixtures of Bose gases of different species. We prove that in the mean field limit and under suitable conditions on the initial condition, a system composed of two Bose species can be effectively described by a system of coupled Hartree equations. Moreover, we derive quantitative bounds on the rates of convergence of the reduced density matrices in Sobolev trace norms. We treat both the non-relativistic case in the presence of an external magnetic field [Formula: see text] and the semi-relativistic case.
arXiv:1702.00827•Reviews in Mathematical Physics•Jul 5, 2017•29 citations