标题： 玻色-劳宾修正与哈特里动力学的迹范数收敛 显示英文标题

标题： Bogoliubov corrections and trace norm convergence for the Hartree dynamics

摘要： 我们研究了大量非相对论性玻色子在平均场极限下的动力学问题，考虑了一类包括库仑相互作用的相互作用势。 为了描述围绕平均场Hartree态的涨落，我们在N粒子空间引入了一个辅助哈密顿量，它与从Bogoliubov理论得到的非常相似。 我们证明了辅助时间演化在N粒子空间范数下收敛到完全相互作用的动力学。 这一结果使我们能够证明若干其他结果：迹范数下约化密度矩阵的收敛，能量迹范数下的收敛，以及收敛到从Fock空间上的Bogoliubov哈密顿量得到的时间演化，且收敛率达到预期的最佳值。 因此，我们扩展并量化了先前的若干结果，例如，提供了具有物理意义的收敛率，包括含时外部场和奇异相互作用，并允许一般的初始态，例如，预期为相互作用系统基态的那些态。 显示英文摘要

摘要： We consider the dynamics of a large number N of nonrelativistic bosons in the mean field limit for a class of interaction potentials that includes Coulomb interaction. In order to describe the fluctuations around the mean field Hartree state, we introduce an auxiliary Hamiltonian on the N-particle space that is very similar to the one obtained from Bogoliubov theory. We show convergence of the auxiliary time evolution to the fully interacting dynamics in the norm of the N-particle space. This result allows us to prove several other results: convergence of reduced density matrices in trace norm with optimal rate, convergence in energy trace norm, and convergence to a time evolution obtained from the Bogoliubov Hamiltonian on Fock space with expected optimal rate. We thus extend and quantify several previous results, e.g., by providing the physically important convergence rates, including time-dependent external fields and singular interactions, and allowing for general initial states, e.g., those that are expected to be ground states of interacting systems.