The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a “good” truncation method, where by “good” we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the “n-particle approximation” to HOPS. We also introduce a new approximation, which we call the “n-mode approximation.” We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

中文翻译：

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灵活的方案以截断纯状态的层次结构

纯态层次（HOPS）是一种基于波函数的方法，可用于对开放量子系统进行数值建模。从形式上讲，HOPS可以为层次结构的无限深度恢复精确的系统动力学。但是，为了数字化地实现HOPS，需要截断层次结构。我们想选择一种“好的”截断方法，其中“好的”表示在数值上检查结果的收敛性是可行的。对于在HOPS的先前应用中使用的截断近似，收敛性检查在数值上具有挑战性。在这项工作中，我们演示了“ n粒子近似”在HOPS中的应用。我们还引入了一个新的近似值，我们称之为“ n模式近似。” 然后，我们针对两个示例性问题：分子聚集体的吸收和能量转移，在层次结构中所需的等式数目上探讨了这些截断近似的收敛性。