BGK model of the multi-species Uehling-Uhlenbeck equation
Gi-Chan Bae, Christian Klingenberg, Marlies Pirner, Seok-Bae Yun
Abstract
<p style='text-indent:20px;'>We propose a BGK model of the quantum Boltzmann equation for gas mixtures. We also provide a sufficient condition that guarantees the existence of equilibrium coefficients so that the model shares the same conservation laws and <inline-formula><tex-math id="M1">\begin{document}$ H $\end{document}</tex-math></inline-formula>-theorem with the quantum Boltzmann equation. Unlike the classical BGK for gas mixtures, the equilibrium coefficients of the local equilibriums for quantum multi-species gases are defined through highly nonlinear relations that are not explicitly solvable. We verify in a unified way that such nonlinear relations uniquely determine the equilibrium coefficients under the condition, leading to the well-definedness of our model. <p style='text-indent:20px;'> <p style='text-indent:20px;'>Erratum: The month information has been corrected from January to February. We apologize for any inconvenience this may cause.