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.