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

Ioannis Anapolitanos, Michael Hott, Dirk Hundertmark

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26 Scopus citations

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 Lloc2(3; 3) and the semi-relativistic case.

Original languageEnglish (US)
Article number1750022
JournalReviews in Mathematical Physics
Volume29
Issue number7
DOIs
StatePublished - Aug 1 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017 World Scientific Publishing Company.

Keywords

  • Mean field limit
  • mixtures of Bose-Einstein condensates

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