The post-inflationary Peccei-Quinn symmetry-breaking scenario provides a rich theoretical frame-
work to study axion dark matter production through the dynamics of topological defects. Accurate
predictions for the axion abundance require a detailed understanding of the formation and evolution of cosmic strings and domain walls, which are inevitably produced in this scenario.
Most existing studies rely on large-scale numerical simulations of the classical equations of mo-
tion, which are subject to significant systematic uncertainties. In this contribution, we briefly
review the main features of the post-inflationary scenario and the current limitations in the literature, and present preliminary results from a new analytical framework for axion domain wall
networks.
Our approach is based on nonequilibrium quantum field theory. It employs the two-particle-
irreducible effective action to derive effective Fokker-Planck equations for macroscopic quantities
such as the average energy density and root-mean-square velocity of the network. We discuss the
relevance of thermal, self-interactions, plasma-induced and quantum effects for cosmological axion abundance estimates, with applications to QCD axions and high-mass axion-like particles.