论文标题
量子不一致系统的PlaneWave近似的收敛性
Convergence of the Planewave Approximations for Quantum Incommensurate Systems
论文作者
论文摘要
不稳定的结构是由于将低维材料的单层堆叠在彼此的基础上，而诸如方向的平面扭曲之类的不对准。尽管这些结构具有重大的身体兴趣，但由于周期性的丧失，它们构成了许多理论上的挑战。在本文中，我们以弱含义的不稳定系统的意义来表征Schrödinger运算符状态的密度，并开发了新颖的数值方法来近似它们。特别是，我们（i）证明了实际空间公式中状态密度的热力学极限； （ii）提出有效的数值方案，以根据PlaneWave近似和相互的空间采样来评估状态的密度。我们介绍了严格的分析和数值模拟，以支持数值算法的可靠性和效率。
Incommensurate structures arise from stacking single layers of low-dimensional materials on top of one another with misalignment such as an in-plane twist in orientation. While these structures are of significant physical interest, they pose many theoretical challenges due to the loss of periodicity. In this paper, we characterize the density of states of Schrödinger operators in the weak sense for the incommensurate system and develop novel numerical methods to approximate them. In particular, we (i) justify the thermodynamic limit of the density of states in the real space formulation; and (ii) propose efficient numerical schemes to evaluate the density of states based on planewave approximations and reciprocal space sampling. We present both rigorous analysis and numerical simulations to support the reliability and efficiency of our numerical algorithms.
