有限体系动力学Bethe-Salpeter方程的实时求解方法
Real-Time Approach to the Dynamical Bethe-Salpeter Equation for Finite Systems
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中文总结 AI 辅助
本研究提出求解动力学Bethe-Salpeter方程的实时线性响应方法，采用时间域乘积计算频率卷积，可兼容随机采样，为超大体系的动力学BSE计算提供了新途径。
中文摘要 AI 辅助
我们提出了一种求解动力学Bethe-Salpeter方程（BSE）的实时线性响应方法。在轨道基组表示框架内，通过单粒子密度矩阵的时间相关Hartree传播，得到屏蔽相互作用的极化部分。定义动力学核的频率卷积以时间域乘积形式计算，避免了数值积分及完整屏蔽库仑算符的存储。随后直接求解所得非线性本征值问题，突破了静态屏蔽近似，实现了屏蔽相互作用的全频率依赖。尽管确定性标度仍为O(N^6)，但该时间传播公式易于与基于网格的随机采样方法兼容，为超大体系的动力学BSE计算开辟了可能。
英文摘要
We present a real-time linear-response approach to solving the dynamical Bethe-Salpeter equation (BSE). The polarization part of the screened interaction is obtained from time-dependent Hartree propagation of the one-particle density matrix within an orbital basis-set representation. The frequency convolution defining the dynamical kernel is evaluated as a product in time, avoiding numerical integration and storage of the full screened Coulomb operator. The resulting nonlinear eigenvalue problem is then solved directly, going beyond the static screening approximation with full-frequency dependence in the screened interaction. While the deterministic scaling remains $\mathcal{O}(N^6)$, the time propagation formulation is readily compatible with grid-based stochastic sampling methods, which will open the possibility for dynamical BSE calculations of very large systems.
