Natural classical limit for the center of mass of many-particle quantum systems

TL;DR

This paper demonstrates that the center of mass of many-particle quantum systems behaves classically under certain conditions, linking Bohmian mechanics with classical trajectories and extending Ehrenfest's theorem.

Contribution

It introduces a condition for classicality of the center of mass in many-particle quantum systems using Bohmian mechanics, unifying quantum and classical descriptions.

Findings

Center of mass follows a classical trajectory under specific conditions.

The classical trajectory is compatible with a nonlinear Schrödinger equation.

Provides a link between Bohmian mechanics and classical physics.

Abstract

We discuss the conditions for the classicality of quantum states with a very large number of identical particles. By treating the center of mass as a Bohmian particle, we show that it follows a classical trajectory when the distribution of the Bohmian positions in just one experiment is always equal to the marginal distribution of the quantum state in physical space. This result can also be interpreted as a unique-experiment generalization of the well-known Ehrenfest theorem. We also demonstrate that the classical trajectory of the center of mass is fully compatible with a conditional wave function solution of a classical non-linear Schr\"odinger equation. Our work shows clear evidence for a quantum-classical inter-theory unification and opens new possibilities for practical quantum computations with decoherence.