Derivation of the Hartree equation for compound Bose gases in the mean field limit

2017/07/05 by Ioannis Anapolitanos, Michael Hott, Dirk Hundertmark · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum, superfluid, helium dynamics #Optical properties and cooling technologies in crystalline materials

paper · doi:10.1142/s0129055x17500222

Abstract

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.

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