Identical Bosons, large occupation numbers and classical field description

Abstract

For a system with a large number of identical Bosons, it is common to claim, often without any additional justifications, that, when the mean occupation number in a single particle state is sufficiently large, classical field description will be applicable. This is why e.g. for ultra-light dark matter, the classical field equations are used to compute its dynamics. In this work, we test the validity and robustness of this assumption based on the criterion $2 \sigma_\varphi < |\langle \varphi \rangle| $ for classical field behaviour and applying it to aribtrary quantum states. We find that an arbitrary state with large occupation number doesn't behave classically while imposing some restrictions on the state vectors can improve the classical behavior. Since coherent states are known to have quasi-classical behaviour, we also ask how much deviation from coherent state can spoil the classical behaviour. Based on this analysis, we find that it is the proximity of the state to a large occupation coherent state rather than large occupation number itself which ensures validity of classical description. Implications of this for ultra light dark matter are discussed.