论文标题
许多粒子相互作用的平均场极限
Mean field limit for many-particle interactions
论文作者
论文摘要
我们提供了一个误差，用于通过广义的非线性hartree方程近似N玻色子的时间演变。假定玻色子通过置换对称有界的多粒子电位相互作用，而初始波功能是乘积状态。我们表明，从追踪完整的N颗粒schrodinger方程而得出的单个粒子的实际演化与平均场近似通用的非线性hartree方程量表的求解为1/n。我们的结果是先前针对有界2粒子电势的情况给出的严格误差界限的概括
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
