论文标题
从阻尼的量子Lorentz气体中衍生线性玻尔兹曼方程，并具有一般散射器构型
Derivation of the linear Boltzmann equation from the damped quantum Lorentz gas with a general scatterer configuration
论文作者
论文摘要
在数学物理学中，是从微观模型中得出宏观传输方程的基本问题。在本文中，我们将线性玻尔兹曼方程以抑制量子洛伦兹气体的低密度极限，用于大量的确定性和随机散射构型。以前，此结果仅因单晶圆环上的单碎片问题而闻名，并且对于不需要阻尼的均匀随机散射构型。阻尼对于建立收敛至关重要 - 在没有阻尼的情况下，限制行为取决于所考虑的确切配置，实际上，线性玻尔兹曼方程预计不会出现在周期性和其他高度有序的配置中。
It is a fundamental problem in mathematical physics to derive macroscopic transport equations from microscopic models. In this paper we derive the linear Boltzmann equation in the low-density limit of a damped quantum Lorentz gas for a large class of deterministic and random scatterer configurations. Previously this result was known only for the single-scatterer problem on the flat torus, and for uniformly random scatterer configurations where no damping is required. The damping is critical in establishing convergence -- in the absence of damping the limiting behaviour depends on the exact configuration under consideration, and indeed, the linear Boltzmann equation is not expected to appear for periodic and other highly ordered configurations.
