标题： 布洛赫电子的渐近分析与韦尔节点 显示英文标题

标题： Asymptotic analysis for Bloch electrons with Weyl nodes

摘要： 在本文中，我们研究了在存在外尔节点的材料能带结构中的布洛赫电子的半经典行为，外尔节点是某些材料能带结构中的奇异点。我们进行了渐近分析，并给出了在存在外尔节点的情况下布洛赫电子电流的半经典渐近展开式的严格推导。分析表明，电流包含两部分，一部分与外尔节点无关，另一部分来自奇异点。这项工作为最近在外尔半金属中的科学发现提供了理论基础。本文的主要创新是一种处理奇异点的新策略，并带有定量估计，这可能在具有奇点的多尺度模型中有更广泛的应用。 显示英文摘要

摘要： In this paper, we study the semiclassical behavior of Bloch electrons in the presence of Weyl nodes, which are singular points in the band structure of certain materials. We carry out asymptotic analysis and present a rigorous derivation of the semiclassical asymptotic expansion of the current of Bloch electrons with the presence of Weyl nodes. The analysis shows that the current contains two parts, one independent of the Weyl nodes and the other a contribution from the singular points. This work provides a theoretical foundation towards a rigorous justification of recent scientific discoveries in Weyl semimetals. The main innovation of this paper is a new strategy to deal with the singular points with quantitative estimates, which may have broader applications in multiscale models with singularities.