Unified description of corpuscular and fuzzy bosonic dark matter II: Dissipation and stochastic forces

TL;DR

This paper develops a comprehensive theoretical framework combining stochastic and dissipative effects in bosonic dark matter, unifying fuzzy and particle-like components through coupled equations derived from quantum field theory.

Contribution

It extends previous models by deriving stochastic, dissipative, and collisional equations for mixed bosonic dark matter from a non-relativistic quantum field approach.

Findings

Derived coupled stochastic Gross-Pitaevskii and Boltzmann equations

Included dissipative and scattering effects in the model

Ensured consistency with fluctuation-dissipation relations

Abstract

We extend our previous work (Proukakis {\em et al.}, Phys.~Rev.~D~108,~083513 (2023)) on the dynamics of bosonic, non-relativistic and self-interacting dark matter that simultaneously contains both a ``fuzzy'' low-momentum component and one with higher momenta that may be well approximated as a collection of distinct particles and described by a corresponding phase-space distribution. Starting from the non-relativistic Schwinger-Keldysh action and working beyond leading-order in the Keldysh basis fields, encoding stochastic fluctuations of the slow modes and all fluctuations of the fast modes, we obtain stochastic self-consistently coupled Gross-Pitaevskii, collisional Boltzmann kinetic and Poisson equations. Our final set of equations, which feature various collisional (dissipative and scattering) contributions and two corresponding independent stochastic force terms, are consistent with generalized fluctuation-dissipation type relations in the limit of thermal equilibrium between the particles.