含磁场的平均场量子动力学
Mean-field quantum dynamics with magnetic fields
摘要：
本文研究了一个三维$N$玻色子系统，系统在外磁场中通过平均场库仑势相互作用。对于初始因式分解态，我们证明了与$N$体薛定谔方程的解相关的单粒子密度矩阵在迹范数和能量上收敛到磁Hartree方程的解上的投影为$N \rightarrow \infty$。估计的收敛速度。
英文摘要：
We consider a system of $N$ bosons in three dimensions interacting through a mean-field Coulomb potential in an external magnetic field. For initially factorized states we show that the one-particle density matrix associated with the solution of the $N$-body Schrödinger equation converges to the projection onto the solution of the magnetic Hartree equation in trace norm and in energy as $N \rightarrow \infty$. Estimates on the rate of convergence are provided.
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