使用自适应和多速率时间积分推进耦合电子和声子非平衡动力学模拟
Advancing Simulations of Coupled Electron and Phonon Nonequilibrium Dynamics Using Adaptive and Multirate Time Integration
AI总结：
本文提出利用自适应和多速率时间积分方法求解耦合电子与声子的实时玻尔兹曼方程，在相同精度下实现10倍加速，大幅扩展了材料非平衡动力学模拟的时间尺度和系统规模。
摘要：
时域电子结构计算提供了对材料非平衡动力学更深入的理解。实时玻尔兹曼方程（rt-BTE）与基于第一性原理计算的精确相互作用相结合，实现了对耦合电子和晶格动力学的可靠预测。然而，该方法可及的时间尺度和系统尺寸仍然有限，主要挑战在于电子和声子相互作用具有不同的时间尺度，以及计算碰撞积分的成本较高。因此，这类计算目前仅有少数实例，主要集中在二维（2D）材料上。在此，我们利用自适应和多速率时间积分方法，在求解电子和声子耦合的 rt-BTE 方程方面取得了重大进展。与常规（非自适应）时间步进方法相比，我们的方法在给定目标精度下实现了 10 倍的加速，或在相同计算成本下将精度提高了 3 到 6 个数量级，从而能够在 2D 和块体材料中进行高效计算。我们通过计算石墨烯中高达约 100 ps 的耦合电子与晶格动力学，以及模拟块体材料（硅）中的超快晶格动力学和热漫散射图，展示了这种高效性。这些结果为材料非平衡物理的定量研究开辟了新机遇。
英文摘要：
Electronic structure calculations in the time domain provide a deeper understanding of nonequilibrium dynamics in materials. The real-time Boltzmann equation (rt-BTE), used in conjunction with accurate interactions computed from first principles, has enabled reliable predictions of coupled electron and lattice dynamics. However, the timescales and system sizes accessible with this approach are still limited, with two main challenges being the different timescales of electron and phonon interactions and the cost of computing collision integrals. As a result, only a few examples of these calculations exist, mainly for two-dimensional (2D) materials. Here we leverage adaptive and multirate time integration methods to achieve a major step forward in solving the coupled rt-BTEs for electrons and phonons. Relative to conventional (non-adaptive) time-stepping, our approach achieves a 10x speedup for a given target accuracy, or greater accuracy by 3-6 orders of magnitude for the same computational cost, enabling efficient calculations in both 2D and bulk materials. This efficiency is showcased by computing the coupled electron and lattice dynamics in graphene up to $\sim$100 ps, as well as modeling ultrafast lattice dynamics and thermal diffuse scattering maps in a bulk material (silicon). These results open new opportunities for quantitative studies of nonequilibrium physics in materials.
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