Bogoliubov corrections and trace norm convergence for the Hartree dynamics

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