Mean field approximation of many-body quantum dynamics for Bosons in a discrete numerical model

The mean field approximation is numerically validated in the bosonic case by considering the time evolution of quantum states and their associated reduced density matrices by many-body Schr\"odinger dynamics. The model phase-space is finite-dimensional. The results are illustrated with numerical simulations of the evolution of quantum states according to the time, the number of the particles, and the dimension of the phase-space.