玻色子星的平均场动力学
Mean Field Dynamics of Boson Stars
摘要：
我们考虑具有相对论色散的N玻色子通过平均场库仑势（吸引或排斥）相互作用的量子力学系统。我们选择初始波函数来描述凝聚体，其中N个玻色子都处于相同的单粒子态。从N体Schroedinger方程出发，证明了在N趋于无穷大的极限下，单粒子密度随时间的演化服从相对论性非线性Hartree方程.这个方程被用来描述玻色子星的动力学（Krasekhar理论）。相应的静态问题由Lieb和Yau严格解决。
英文摘要：
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.
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