截断纯态层次的灵活方案
Flexible scheme to truncate the hierarchy of pure states
摘要：
纯态体系（HOPS）是一种基于波函数的方法，可用于开放量子系统的数值模拟。形式上，HOPS恢复了精确的系统动力学的层次结构的无限深度。然而，需要截断的层次结构，以数字实现HOPS。我们希望选择一个“好”的截断方法，这里的“好”是指在数值上检查结果的收敛性是可行的。对于截断近似在以前的应用程序中使用的HOPS，收敛性检查是数值上的挑战。在这项工作中，我们证明了应用“$n$ -粒子近似”（$n$ PA）HOPS。我们还介绍了一种新的近似，我们称之为“$n$模式近似”（$n$ MA）。然后，我们探讨这些截断近似的收敛性方面所需的方程的层次结构。我们表明，截断近似可以结合使用，以实现收敛的两个示例性的问题：吸收和能量转移的分子聚集体。
英文摘要：
The hierarchy of pure states (HOPS) is a wavefunction-based method which 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' ($n$PA) to HOPS. We also introduce a new approximation, which we call the '$n$-mode approximation' ($n$MA). We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy. We show that truncation approximations can be used in combination to achieve convergence in two exemplary problems: absorption and energy transfer of molecular aggregates.
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