AI 中文总结
本文提出了适用于非马尔可夫量子动力学的通用朗之万框架，将其应用于延迟相干反馈问题，重现并预测了激光线宽的窄化效应，且框架可扩展至多体系统。
AI 中文摘要
相空间方法是处理马尔可夫开放量子系统的强大工具：它们将与环境E相互作用的系统S的约化动力学精确映射为c数随机变量的朗之万方程，而非算符的海森堡-朗之万方程。朗之万方程在关键区域提供解析洞察，且擅长处理强非线性与耦合，而其他方法常在此类场景失效。然而，将相空间方法扩展至非马尔可夫动力学长期以来仍是一项挑战。本文通过将相空间表示应用于完整的S+E系统来解决这一缺口；对环境自由度进行积分后，得到了适用于S的通用朗之万框架，该框架包含来自E的确定性与随机贡献。正规序表示，如Glauber-Sudarshan P表示以及Drummond和Gardiner提出的正P表示，所导出的朗之万方程具有以下特性：（i）非马尔可夫效应仅通过记忆核出现在确定性项中；（ii）当E初始处于真空态时，噪声贡献消失。为展示该框架的效力，本文研究了延迟相干反馈这一范例性问题，其中系统由自身过去的状态驱动，并探究其对激光线宽的影响：我们重现了阈值上方远区观测到的线宽窄化现象，并预测阈值上方紧邻区域存在增强的窄化效应。至关重要的是，随机变量的数量随系统大小线性缩放，这使得该框架适用于从少数自由度到真正多体系统的各类问题。这为利用长期以来使相空间方法在马尔可夫区域取得成功的相同解析与数值工具，系统研究非马尔可夫受驱耗散量子系统开辟了道路。
英文摘要
Phase-space methods are powerful tools for the treatment of Markovian open quantum systems: they map the reduced dynamics of a system S, in interaction with an environment E, exactly onto Langevin equations for c-number stochastic variables, as opposed to Heisenberg-Langevin equations for operators. Langevin equations provide analytical insight in key regimes and excel at handling strong nonlinearities and couplings, where other methods often falter. Extending phase-space methods to non-Markovian dynamics, however, has remained a long-standing challenge. Here we address this gap by applying phase-space representations to the full S+E system; integrating out the environmental degrees of freedom then yields a general Langevin framework for S that incorporates both deterministic and stochastic contributions from E. Normally ordered representations, such as the Glauber-Sudarshan P representation and its positive variant due to Drummond and Gardiner, lead to Langevin equations in which (i) non-Markovian effects emerge exclusively in the deterministic terms, via a memory kernel, and (ii) noise contributions vanish when E is initially in the vacuum state. To demonstrate the power of this framework, we address the paradigmatic problem of delayed coherent feedback, in which the system is driven by its own past state, and study its impact on the laser linewidth: we recover the narrowing observed well above threshold and predict an enhanced narrowing just above it. Crucially, the number of stochastic variables scales linearly with the system size, making the framework suitable for problems ranging from a few degrees of freedom to genuinely many-body systems. This opens the way to the systematic study of non-Markovian driven-dissipative quantum systems using the same analytical and numerical tools that have long made phase-space methods so successful in the Markovian regime.
