Position-Momentum Uncertainty Relation for an Open Macroscopic Quantum System

TL;DR

This paper investigates how the Heisenberg position-momentum uncertainty relation applies to a macroscopic quantum oscillator interacting with environmental particles, showing violations occur with few particles but are resolved with more environmental degrees of freedom.

Contribution

It demonstrates the conditions under which the original uncertainty relation holds or breaks down for macroscopic systems interacting with environments.

Findings

Violation of uncertainty relation with few environmental particles

Increasing environmental degrees of freedom restores the relation

Results are relevant for quasi-classical macroscopic quantum systems

Abstract

In this study, we explore the validity of the original Heisenberg position- momentum uncertainty relation for a macroscopic harmonic oscillator interacting with environmental micro particles. Our results show that, in the quasi-classical situation, the original uncertainty relation does not hold when the number of particles in the environment is small. Nonetheless, increasing the environmental degrees of freedom resolves the violation in the region of our investigation.