We consider a kinetic model of an N-species gas mixture modeled with quantum Bhatnagar-Gross-Krook (BGK) collision operators. The collision operators consist of a relaxation to a Maxwell distribution in the classical case, a Fermi distribution for fermions and a Bose-Einstein distribution for bosons. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function. This is motivated by theoretical considerations coming from entropy minimization. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method presented in this paper, and illustrate its usefulness and effectiveness with numerical examples

翻译：本文考虑一个由量子Bhatnagar-Gross-Krook（BGK）碰撞算子建模的N种气体混合物动力学模型。碰撞算子包括经典情形下向麦克斯韦分布的松弛、费米子的费米分布以及玻色子的玻色-爱因斯坦分布。我们提出了一种用于模拟该模型的数值方法，该方法采用隐式-显式（IMEX）格式以最小化某个特定势函数，这一思路源于熵最小化的理论考量。我们证明，本文提出的数值方法保持了质量、总动量与总能量的守恒性以及分布函数的正定性，并通过数值算例展示了其实用性与有效性。