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

Anapolitanos, Ioannis; Hott, Michael; Hundertmark, Dirk

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 ∈ L2 loc(R3;R3) and the semi-relativistic case.


Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2017
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000068126
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-681262
KITopen ID: 1000068126
Verlag KIT, Karlsruhe
Umfang 24 S.
Serie CRC 1173 ; 2017/7
Schlagworte compound Bose gases, mean field limit, Sobolev trace norms
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