Abstract Scalar dark Lower Membrane matter (DM), and axions in particular, have an irreducible abundance of particles produced by freeze-in due to portal interactions with the Standard Model plasma in the early Universe.In addition, vacuum misalignment and other mechanisms can lead to the presence of a cold, oscillating condensate.Therefore, generically, the evolution of the DM in both forms, condensate and particles, needs to be studied simultaneously.In non-equilibrium quantum field theory, the condensate and particles are described by one- and two-point functions, respectively.The fundamental coupled equations of motion (EoMs) of these objects are non-local.
To simplify the EoMs Vinyl Patch Kits and bring them into a familiar form for relic abundance calculations, we perform a Markovianization process for a quasi-harmonically oscillating homogeneous condensate, leading to local EoMs for the particle distribution function and the envelope function of condensate oscillation.This reduces the dynamics to a pair of coupled Boltzmann equations, and we derive explicitly the form of the collision operators for all particle and condensate interactions.