Alexander Elgart and Benjamin Schlein
Mean Field Dynamics of Boson Stars
(123K, LateX)
ABSTRACT. 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
Schroedinger equation, we prove that, in the limit N goes to infinity, 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 by Lieb and Yau.