含时随机Bethe-Salpeter方法
Time-dependent Stochastic Bethe-Salpeter Approach
摘要：
基于Bethe-Salpeter方程（BSE），利用随机波函数方法，建立了扩展有限系统中电子空穴激发的含时公式.含时公式建立在含时Hartree-Fock（TDHF）理论和单取代构型相互作用（CIS）方法之间的联系上。这导致一个依赖于时间的类薛定谔方程的准粒子轨道动力学的基础上的有效哈密顿包含直接哈特里和屏蔽交换条款，其中屏蔽内描述的随机相位近似（RPA）。为了解决光吸收谱，我们开发了一个随机配方，其中准粒子轨道被随机轨道取代，以评估直接和交换项的哈密顿量以及RPA屏蔽。这导致了一个整体的二次缩放，一个显着的改善，相当于辛特征值表示的BSE。应用时间相关的随机BSE（TDsBSE）的方法，硅和CdSe纳米晶体的大小~3000电子的介绍和讨论。
英文摘要：
A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the connection between time-dependent Hartree-Fock (TDHF) theory and configuration-interaction with single substitution (CIS) method. This results in a time dependent Schrödinger-like equation for the quasiparticle orbital dynamics based on an effective Hamiltonian containing direct Hartree and screened exchange terms, where screening is described within the Random Phase Approximation (RPA). To solve for the optical absorption spectrum, we develop a stochastic formulation in which the quasiparticle orbitals are replaced by stochastic orbitals to evaluate the direct and exchange terms in the Hamiltonian as well as the RPA screening. This leads to an overall quadratic scaling, a significant improvement over the equivalent symplectic eigenvalue representation of the BSE. Application of the time-dependent stochastic BSE (TDsBSE) approach to silicon and CdSe nanocrystals up to size of ~3000 electrons is presented and discussed.
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