On the single classical field description of interacting scalar fields

TL;DR

This paper investigates how well interacting bosonic systems can be approximated by classical fields as occupation numbers grow, analyzing quantum corrections and the conditions affecting convergence.

Contribution

It provides a systematic analysis of the quantum breaktime in various models and initial states, revealing how interactions and initial conditions influence classical approximation validity.

Findings

Number eigenstates do not converge to classical evolution with increasing occupation.

Systems similar to scalar dark matter show logarithmic quantum breaktime scaling.

Contact interactions and certain initial states exhibit power-law scaling of quantum breaktime.

Abstract

We test the degree to which interacting Bosonic systems can be approximated by a classical field as total occupation number is increased. This is done with our publicly available code repository, \href{https://github.com/andillio/QIBS}{QIBS}, a massively parallel solver for these systems. We use a number of toy models well studied in the literature and track when the classical field description admits quantum corrections, called the quantum breaktime. This allows us to test claims in the literature regarding the rate of convergence of these systems to the classical evolution. We test a number of initial conditions, including coherent states, number eigenstates, and field number states. We find that of these initial conditions, only number eigenstates do not converge to the classical evolution as occupation number is increased. We find that systems most similar to scalar field dark matter exhibit a logarithmic enhancement in the quantum breaktime with total occupation number. Systems with contact interactions or with field number state initial conditions, and linear dispersions, exhibit a power law enhancement. Finally, we find that the breaktime scaling depends on both model interactions and initial conditions.