Boltzmann equation plays important roles in particle cosmology in studying the evolution of distribution functions (also called as occupation numbers) of various particles. For the case of the decay of a scalar condensation $ϕ$ into a pair of scalar particles (called $χ$), we point out that the system may not be well described by the Boltzmann equation when the occupation number of $χ$ becomes large even in the so-called narrow resonance regime. We study the particle production including the possible enhancement due to a large occupation number of the final state particle, known as the stimulated emission or the parametric resonance. Based on the quantum field theory (QFT), we derive a set of equations which directly govern the evolution of the distribution function of $χ$. Comparing the results of the QFT calculation and those from the Boltzmann equation, we find non-agreements in some cases. In particular, in the expanding Universe, the occupation number of $χ$ based on the QFT may differ by many orders of magnitude from that from the Boltzmann equation. We also discuss a possible relation between the evolution equations based on the QFT and the Boltzmann equation.
Graviton Production from Inflaton Condensate: Boltzmann vs Bogoliubov
Bethe Center for Theoretical Physics and Physikalisches Institut Universität Bonn（波恩大学贝特理论物理中心与物理研究所）；McGill University Department of Physics & Trottier Space Institute（麦吉尔大学物理系与特罗蒂尔太空研究所）；International Centre for Theoretical Physics Asia-Pacific, University of Chinese Academy of Sciences（中国科学院大学亚太理论物理中心）；Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS)（中国科学院大学太极引力波宇宙实验室（北京/杭州））
(2+2)D Collective Model based on a relativistic Boltzmann equation in the Isotropization Time Approximation: CoMBolt-ITA
TUM School of Natural Sciences, Technische Universität München（慕尼黑工业大学自然科学学院）；School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所粒子与加速器学院）
Global equilibrium at order $\mathcal{O}(\hbar^2)$: pseudo-gauge ambiguity, Maxwell relations, and thermodynamic consistency
Institut für Theoretische Physik, Johann Wolfgang Goethe–Universität（法兰克福歌德大学理论物理研究所）；Institute of Nuclear Physics Polish Academy of Sciences（波兰科学院核物理研究所）；Helmholtz Research Academy Hesse for FAIR（黑森FAIR亥姆霍兹研究院）
