Single classical field description of interacting scalar fields

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, QIBS, a new 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.

Automated summary

The study examines the approximation of interacting Bosonic systems by classical fields as total occupation number increases, using a new parallel solver QIBS. Different toy models are tested to track quantum corrections in the classical field description, finding that only number eigenstates do not converge to classical evolution with increased occupation number. The scaling of the quantum breaktime depends on model interactions and initial conditions, with some systems exhibiting logarithmic enhancement and others showing power law enhancement.