用于非马尔可夫随机薛定谔方程的低秩分层框架及收敛性分析
A low-rank hierarchical framework for the non-Markovian stochastic Schrödinger equation with convergence analysis
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中文总结 AI 辅助
针对非马尔可夫随机薛定谔方程，提出基于浴关联函数低秩近似的数值框架，通过分解记忆核导出分层方程组，经收敛性分析证明是HOPS的推广，数值实验验证了该方法的有效性和效能。
中文摘要 AI 辅助
我们基于浴关联函数的低秩近似，为非马尔可夫随机薛定谔方程（NMSSE）提出并分析了一种新的数值框架。通过将记忆核分解为有限维表示，我们导出了一个截断的分层方程组，有效平衡了计算可处理性与物理保真度。在温和假设下对分层框架进行了严格的收敛性分析。我们证明我们的公式是纯态层次结构（HOPS）的数学推广，将其作为特殊情况包含在内，同时提供了对非马尔可夫效应更灵活的表示。给出了几个基准模型的数值实验，以说明所提方法的有效性和效能。
英文摘要
We propose and analyze a novel numerical framework for the non-Markovian stochastic Schrödinger equation (NMSSE) based on a low-rank approximation of the bath correlation functions. By decomposing the memory kernel into a finite-dimensional representation, we derive a truncated system of hierarchical equations that effectively balances computational tractability with physical fidelity. A rigorous convergence analysis is established for the hierarchical framework under mild assumptions. We demonstrate that our formulation serves as a mathematical generalization of the Hierarchy of Pure States (HOPS), encompassing it as a special case while offering a more flexible representation of non-Markovian effects. Numerical experiments across several benchmark models are presented to illustrate the validity and efficacy of the proposed method.
