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.
Highlights
Axions or axionlike particles are highly motivated candidates for dark matter
For m ≲ 10−18 eV, tclassical is less than tlinear, i.e., the quantum evolution of the number density differs from the classical evolution within the linear regime
The classical evolution is uniquely determined once the initial density and velocity field are specified
Summary
Axions or axionlike particles are highly motivated candidates for dark matter (see e.g., [1,2,3,4,5,6]). We investigate whether the density and velocity field of axions evolve differently in quantum and classical field treatments. In the classical field approximation, the evolution of the axion fluid is uniquely specified by initial values of the number density nðx⃗ ; 0Þ and the velocity field v⃗ ðx⃗ ; 0Þ. We show that the evolution of axion number density in the quantum field description is not unique for given initial values of number density nðx⃗ ; 0Þ and velocity field v⃗ ðx⃗ ; 0Þ. III, we consider a toy model of axions in a one-dimensional box Using both classical and quantum field theories, we find the growth of density perturbations under the gravitational potential of a static point mass.
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