Mean field dynamics of boson stars

Alexander Elgart, Benjamin Schlein

Research output: Contribution to journalArticlepeer-review

196 Scopus citations


We consider a quantum mechanical system of N bosons with relativistic dispersion interacting through a mean field Coulomb potential (attractive or repulsive). We choose the initial wave function to describe a condensate where the N bosons are all in the same one-particle state. Starting from the N-body Schrödinger equation, we prove that, in the limit N → ∞, the time evolution of the one-particle density is governed by the relativistic nonlinear Hartree equation. This equation is used to describe the dynamics of boson stars (Chandrasekhar theory). The corresponding static problem was rigorously solved in [10].

Original languageEnglish
Pages (from-to)500-545
Number of pages46
JournalCommunications on Pure and Applied Mathematics
Issue number4
StatePublished - 1 Apr 2007
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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