Density perturbations in axion-like particles: classical vs quantum field treatment

TL;DR

This paper compares classical and quantum field treatments of axion-like particles, revealing conditions under which their density perturbation evolutions agree or diverge, especially when multiple quantum states are involved.

Contribution

It demonstrates that quantum and classical evolutions of axion density perturbations differ when multiple quantum states are occupied, highlighting the importance of quantum effects.

Findings

Classical and quantum evolutions are identical with single-particle state occupation.

Quantum evolutions diverge from classical predictions when multiple states are occupied.

Divergence time depends on system parameters.

Abstract

Axions and axion-like particles are bosonic quantum fields. They are often assumed to follow classical field equations due to their high degeneracy in the phase space. In this work, we explore the disparity between classical and quantum field treatments in the context of density and velocity fields of axions. Once the initial density and velocity field are specified, the evolution of the axion fluid is unique in the classical field treatment. However, in the quantum field treatment, there are many quantum states consistent with the given initial density and velocity field. We show that evolutions of the density perturbations for these quantum states are not necessarily identical and, in general, differ from the unique classical evolution. To illustrate the underlying physics, we consider a system of large number of bosons in a one-dimensional box, moving under the gravitational potential of a heavy static point-mass. We ignore the self-interactions between the bosons here. Starting with homogeneous number density and zero velocity field, we determine the density perturbations in the linear regime in both quantum and classical field theories. We find that classical and quantum evolutions are identical in the linear regime if only one single-particle state is occupied by all the bosons and the self-interaction is absent. If more than one single-particle states are occupied, the density perturbations in quantum evolutions differ from the classical prediction after a certain time which depends upon the parameters of the system.