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Mean field dynamics of boson stars
Author(s) -
Elgart Alexander,
Schlein Benjamin
Publication year - 2007
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20134
Subject(s) - chandrasekhar limit , boson , physics , mean field theory , coulomb , limit (mathematics) , field (mathematics) , wave function , stars , hartree , quantum mechanics , classical mechanics , mathematical physics , mathematics , white dwarf , mathematical analysis , astronomy , pure mathematics , electron
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]. © 2005 Wiley Periodicals, Inc.