We review our recent quantum stochastic model for spectroscopic lineshapes in the presence of a coevolving and nonstationary background population of excitations. Starting from a field theory description for interacting bosonic excitons, we derive a reduced model whereby optical excitons are coupled to an incoherent background via scattering as mediated by their screened Coulomb coupling. The Heisenberg equations of motion for the optical excitons are then driven by an auxiliary stochastic population variable, which we take to be the solution of an Ornstein–Uhlenbeck process. Here, we present an overview of the theoretical techniques we have developed as applied to predicting coherent nonlinear spectroscopic signals. We show how direct (Coulomb) and exchange coupling to the bath give rise to distinct spectral signatures and discuss mathematical limits on inverting spectral signatures to extract the background density of states.

中文翻译：

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多体激子散射中随机过程的光学特征

我们回顾了我们最近在存在共同演化和非平稳背景激发群的情况下光谱线形的量子随机模型。从相互作用的玻色子激子的场论描述开始，我们推导出一个简化模型，其中光学激子通过由其屏蔽库仑耦合介导的散射耦合到非相干背景。然后，光学激子的海森堡运动方程由辅助随机布居变量驱动，我们将其视为奥恩斯坦-乌伦贝克过程的解。在这里，我们概述了我们开发的用于预测相干非线性光谱信号的理论技术。我们展示了与浴的直接（库仑）耦合和交换耦合如何产生不同的光谱特征，并讨论了反转光谱特征以提取状态背景密度的数学限制。