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arXiv · 1702.00827

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

Ioannis Anapolitanos·Michael Hott·Dirk Hundertmark
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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 $A\in L^2_{\text{loc}}(\R^3;\R^3)$ and the semi-relativistic case.

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Ioannis Anapolitanos, Michael Hott, Dirk Hundertmark. 2017-02-02. Derivation of the Hartree equation for compound Bose gases in the mean field limit. https://doi.org/10.1142/s0129055x17500222

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