标题： 基准测试 TCL4：评估四阶近似的可用性和可靠性 显示英文标题

标题： Benchmarking TCL4: Assessing the Usability and Reliability of Fourth-Order Approximations

摘要： 开放量子系统的非马尔可夫动力学可以使用费曼-弗纳布隆影响泛函方法严格推导出来。 尽管这种形式化方法是精确的，但实际的数值实现通常需要做出妥协。 时间卷积无（TCL）主方程提供了一个精确的框架，但其应用通常依赖于时间正向和时间反向状态传播器的微扰展开。 由于涉及大量的计算工作——以及大多数开放量子系统缺乏解析解——四阶微扰TCL生成器（TCL4）仅在有限的系统和参数空间中进行了基准测试。 然而，最近的进步使得TCL4的计算更快且更容易实现。 在本文中，我们将TCL4主方程与偏置自旋-玻色模型的数值精确方法进行基准比较。 我们关注接近临界浴耦合的区域，在该区域内微扰主方程预计会变得不准确。 我们的研究结果表明，TCL4方法在低温下最为可靠，并且比数值精确方法更高效。 本研究旨在明确TCL4微扰主方程在何种条件下能提高TCL2的准确性。 显示英文摘要

摘要： The non-Markovian dynamics of an open quantum system can be rigorously derived using the Feynman-Vernon influence functional approach. Although this formalism is exact, practical numerical implementations often require compromises. The time-convolutionless (TCL) master equation offers an exact framework, yet its application typically relies on a perturbative expansion of both the time forward and time backward state propagators. Due to the significant computational effort involved - and the scarcity of analytical solutions for most open quantum systems - the fourth-order perturbative TCL generator (TCL4) has only been benchmarked on a limited range of systems and parameter spaces. Recent advancements, however, have made the computation of TCL4 faster and more accessible. In this paper, we benchmark the TCL4 master equation against numerically exact methods for the biased spin-boson model. We focus on the regime near critical bath coupling where perturbative master equations are expected to become inaccurate. Our findings reveal that the TCL4 approach is most reliable at low temperature and more efficient than the numerical exact methods. This study aims to delineate the conditions under which the TCL4 perturbative master equation enhances the accuracy of the TCL2.