非马尔可夫量子态扩散的通用一阶和二阶数值求解器
A General First- and Second-Order Numerical Solver for Non-Markovian Quantum State Diffusion
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中文总结 AI 辅助
研究非马尔可夫开放量子系统数值模拟难题，基于线性NMQSD方程解析解构建通用辅助态框架，分离数值构建步骤，给出一阶和二阶格式及跃迁规则，经数值结果验证方法对不同情况的适用性。
中文摘要 AI 辅助
基于非马尔可夫量子态扩散（NMQSD）方程对非马尔可夫开放量子系统进行数值模拟时，因关于随机过程的泛函导数而变得复杂，目前仍缺乏直接处理这些泛函导数且不依赖于体系关联函数特定分解的通用数值框架。本文推导了线性NMQSD方程的解析解，揭示了非马尔可夫随机动力学的三种基本结构。基于此构建了针对任意体系关联函数的通用辅助态框架，将数值构建分为时间离散、记忆求积和层次截断。接着构建了一阶和二阶格式并给出显式实现的图形化跃迁规则。数值结果验证了预期的时间精度，并证明了所提方法对不同体系关联函数和多能级量子系统的适用性。
英文摘要
The numerical simulation of non-Markovian open quantum systems based on the non-Markovian quantum state diffusion (NMQSD) equation is complicated by functional derivatives with respect to the stochastic process. A general numerical framework that directly treats these functional derivatives without relying on prescribed decompositions of the bath correlation function is still lacking. In this work, we derive an analytical solution of the linear NMQSD equation that reveals three elementary structures of the non-Markovian stochastic dynamics: stochastic propagation, functional-derivative insertion, and memory pairing. Based on this structure, we construct a general auxiliary-state framework for arbitrary bath correlation functions. The framework separates the numerical construction into time discretization, memory quadrature, and hierarchy truncation. We then construct first- and second-order schemes and provide diagrammatic transition rules for their explicit implementation. Numerical results verify the expected temporal accuracy and demonstrate the applicability of the proposed methods to different bath correlation functions and multi-level quantum systems.
