The classical dynamics for the center of mass of a large quantum system

Abstract

The understanding of the quantum-to-classical transition is of profound significance for the foundations of quantum physics and for practical applications. We propose a protocol for a set of quantum particles to follow classical dynamics by looking at the motion of their center of mass. We show that when the number of a system of particles with non-zero mass is large enough, the center of mass moves along a classical trajectory. The classicality of the center of mass is ensured twofold: It has a definite (initial) position and momentum and follows Newton's law of motion. Our work shows clear evidence for the unification of quantum- and classical-mechanics.