Field moment expansion method for interacting Bosonic systems

TL;DR

The paper presents a numerical method called the field moment expansion for simulating interacting Bosonic systems beyond mean field theory, enabling estimation of quantum breaktimes with improved accuracy.

Contribution

It introduces a second order extension of classical field theory, implemented as a Python package, to better approximate quantum dynamics of Bosonic systems.

Findings

Method accurately estimates quantum breaktime.

Success depends on initial classical description and hierarchical growth of moments.

Validated on scalar field dark matter-like systems.

Abstract

We introduce a numerical method and python package, https://github.com/andillio/CHiMES, that simulates quantum systems initially well approximated by mean field theory using a second order extension of the classical field approach. We call this the field moment expansion method. In this way, we can accurately approximate the evolution of first and second field moments beyond where the mean field theory breaks down. This allows us to estimate the quantum breaktime of a classical approximation without any calculations external to the theory. We investigate the accuracy of the field moment expansion using a number of well studied quantum test problems. Interacting Bosonic systems similar to scalar field dark matter are chosen as test problems. We find that successful application of this method depends on two conditions: the quantum system must initially be well described by the classical theory, and that the growth of the higher order moments be hierarchical.