标题： 周期结构中具有能带交叉的辐射传输 显示英文标题

标题： Radiative transport in a periodic structure with band crossings

摘要： 我们使用Wigner变换和渐近分析，系统地推导出具有任意空间维度和任何周期结构的薛定谔方程的半经典模型。 我们的特别重点在于解决\textit{绝热}效应，即布洛赫带交叉的影响。 我们考虑了确定性和随机情况。 在前一种情况下，我们推导出一个耦合的Liouville系统，揭示了不同布洛赫带之间的低阶相互作用。 在后一种情况下，出现了一个由随机不均匀性引起的辐射输运方程的耦合系统，其散射截面由随机不均匀性产生。 作为具体应用，我们推导了在随机性存在的情况下石墨烯中波包的有效动力学。 显示英文摘要

摘要： We use the Wigner transformation and asymptotic analysis to systematically derive the semi-classical model for the Schr\"{o}dinger equation in arbitrary spatial dimensions, with any periodic structure. Our particular emphasis lies in addressing the \textit{diabatic} effect, i.e., the impact of Bloch band crossings. We consider both deterministic and random scenarios. In the former case, we derive a coupled Liouville system, revealing lower-order interactions among different Bloch bands. In the latter case, a coupled system of radiative transport equations emerges, with the scattering cross-section induced by the random inhomogeneities. As a specific application, we deduce the effective dynamics of a wave packet in graphene with randomness.