Classicality of the order parameter during a phase transition

TL;DR

This paper investigates how the order parameter transitions from quantum to classical during second order phase transitions, using toy models and analyzing environmental effects to understand classicality emergence.

Contribution

It provides a detailed analysis of the quantum-to-classical transition of the order parameter, highlighting the role of environmental interactions and questioning large N approximations.

Findings

Wave packet dynamics show classical behavior emerges over time.

Environmental effects significantly influence the quantum-to-classical transition.

Large N approximation may oversimplify the classicality of the order parameter.

Abstract

We analyze the quantum to classical transition of the order parameter in second order phase transitions. We consider several toy models in non relativistic quantum mechanics. We study the dynamical evolution of a wave packet initially peaked around a local maximum of the potential using variational approximations and also exact numerical results. The influence of the environment on the evolution of the density matrix and the Wigner function is analyzed in great detail. We also discuss the relevance of our results to the analysis of phase transitions in field theory. In particular, we argue that previous results about classicality of the order parameter in O(N) models may be consequences of the large $N$ approximation.