多粒子相互作用的平均场极限
Mean field limit for many-particle interactions
摘要：
本文给出了用广义非线性Hartree方程近似N玻色子时间演化的误差界。假设玻色子通过置换对称有界多粒子势相互作用，初始波函数为乘积态。我们证明了在所有的时间内，由追踪完整的N粒子薛定谔方程得到的单个粒子的实际演化与平均场近似广义非线性Hartree方程的解之间的误差为1/N。我们的结果是以前给出的有界二粒子势严格误差界的推广
英文摘要：
We provide an error bound for approximating the time evolution of N bosons by a generalized nonlinear Hartree equation. The bosons are assumed to interact via permutation symmetric bounded many-particle potentials and the initial wave-function is a product state. We show that the error between the actual evolution of a single particle derived from tracing out the full N-particle Schrodinger equation and the solution to the mean field approximate generalized nonlinear Hartree equation scales as 1/N for all times. Our result is a generalization of rigorous error bounds previously given for the case of bounded 2-particle potentials
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