量子涨落与平均场动力学的收敛速度
Quantum Fluctuations and Rate of Convergence towards Mean Field Dynamics
摘要：
非线性Hartree方程描述了初始因式分解的N玻色子态的宏观动力学，在大N的极限下。在本文中，我们提供的收敛速度的微观量子力学演化的极限Hartree动力学的估计。更确切地说，我们证明了与N体薛定谔方程的解和正交投影到Hartree方程的解之间的差异的一个粒子密度的界限。
英文摘要：
The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized N-boson states, in the limit of large N. In this paper we provide estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting Hartree dynamics. More precisely, we prove bounds on the difference between the one-particle density associated with the solution of the N-body Schroedinger equation and the orthogonal projection onto the solution of the Hartree equation.
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