论文标题
相对论量子玻尔兹曼方程在平衡附近
The relativistic quantum Boltzmann equation near equilibrium
论文作者
论文摘要
相对论的量子玻尔兹曼方程（或相对论的uehling-uhlenbeck方程）描述了单个特性快速移动量子粒子的动力学。随着相对论量子力学的最新发展，相对论量子玻尔兹曼方程已被广泛用于物理和工程中，例如在量子碰撞实验和石墨烯中电子的模拟中。尽管如此重要，但对于最佳作者知识的相对论量子玻尔兹曼方程的解决方案的存在仍然没有数学理论。在本文中，当初始分布在附近的全局平衡附近时，我们证明了对相对论玻尔兹曼方程的全球经典解决方案的全球存在。
The relativistic quantum Boltzmann equation (or the relativistic Uehling-Uhlenbeck equation) describes the dynamics of single-species fast-moving quantum particles. With the recent development of the relativistic quantum mechanics, the relativistic quantum Boltzmann equation has been widely used in physics and engineering such as in the quantum collision experiments and the simulations of electrons in graphene. In spite of such importance, there has been no mathematical theory on the existence of solutions for the relativistic quantum Boltzmann equation to the best of authors' knowledge. In this paper, we prove the global existence of a unique classical solution to the relativistic Boltzmann equation for both bosons and fermions when the initial distribution is nearby a global equilibrium.
