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

TL;DR

This paper numerically validates the mean field approximation for bosonic quantum dynamics in a finite-dimensional phase-space, using simulations of many-body Schrödinger evolution and reduced density matrices.

Contribution

It introduces a numerical validation of the mean field approximation for bosons within a finite-dimensional phase-space model.

Findings

Mean field approximation accurately predicts quantum state evolution.

Validation across different particle numbers and phase-space dimensions.

Numerical simulations confirm theoretical expectations.

Abstract

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.