发表机构
University of Freiburg; California Institute of Technology; The Hebrew University of Jerusalem; University of California, Berkeley（弗赖堡大学; 加州理工学院; 耶路撒冷希伯来大学; 加利福尼亚大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对HEOM方法在强耦合玻色子浴中的数值不稳定性，提出非酉相似变换平衡层级项，显著扩大可模拟的系统-浴耦合范围。
AI 中文摘要
分层运动方程（HEOM）方法是模拟开放量子系统动力学的最强大方法之一。尽管HEOM方法在许多参数区域和物理场景中已被证明是稳定且高效的，但众所周知，对层级不可避免的有限截断可能导致玻色子环境中的基本数值不稳定性。在本工作中，我们应用最近发展的技术来分析这些问题。我们利用层级的辅助福克空间图像，首先识别出不平衡的层级提升项，这些项导致了与HEOM生成器的非正态代数结构相关的强瞬态放大。随后，我们应用一个非酉相似变换，将这些项转化为层级提升项和层级降低项的平衡组合，从而抑制其数值影响。我们首先通过一个具有简单布朗振子谱密度的自旋-玻色子模型展示该方法的有效性，随后将分析扩展到结构化谱密度，表明在两种情况下，变换后的HEOM方法都允许模拟比原本可能实现的更大的系统-浴耦合。
英文摘要
The hierarchical equations of motion (HEOM) approach is one of the most powerful methods avail- able to simulate the dynamics of open quantum systems. Although the HEOM approach has been shown to be stable and efficient in many parameter regimes and physical scenarios, it is also well known that the unavoidable finite truncation of the hierarchy can lead to fundamental numeri- cal instabilities for bosonic environments. In this work, we apply recently developed techniques to analyze these issues. We use an auxiliary Fock-space picture of the hierarchy to first identify the unbalanced hierarchy-raising terms responsible for the strong transient amplification associated with the non-normal algebraic structure of the HEOM generator. We then apply a non-unitary similarity transformation that converts these terms into balanced combinations of hierarchy-raising and hierarchy-lowering terms, thereby suppressing their numerical impact. We first demonstrate the efficacy of this approach via a spin-boson model with a simple Brownian oscillator spectral den- sity and subsequently extend the analysis to a structured spectral density, showing for both cases that the transformed HEOM approach allows simulations of much larger system-bath coupling than would otherwise be possible.
