发表机构
University of Rochester（罗切斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究开发对称性适配的HEOM形式，降低HTC模型计算成本，通过去除ADO冗余信息，在保证动力学精度的同时减少所需变量与内存，可扩展至多类场景。
AI 中文摘要
分层运动方程（HEOM）可提供与谐波库耦合的开放量子体系的精确动力学，但对于具有多个独立局域环境的体系，其计算成本会变得过高。本研究开发了一种对称性适配的HEOM形式，以显著降低置换不变的Holstein-Tavis-Cummings（HTC）模型的计算成本。该方法分两个阶段去除冗余信息：第一阶段，所有仅通过重新标记相同分子及其库通道关联的辅助密度算子（ADO）被替换为单一的正则占据模式代表；第二阶段，具有相同局域层级占据的分子在每个代表内产生重复的矩阵元，因此仅需传播不同的复变量，而非完整的（N + 1）×（N + 1）ADO矩阵。所得的无矩阵方程通过预计算的连接和分子多重性进行评估。在固定层级深度L和库相关指数数量m的情况下，当N ≥ L时，正则代表的数量与系综大小无关；当N ≥ L + 2时，唯一变量的数量达到饱和。该形式可轻松扩展至多指数库分解、任意初始密度算子、静态无序和腔损耗。我们的基准测试重现了传统HEOM的动力学，同时需要传播的变量少得多，且内存需求大幅降低。
英文摘要
Hierarchical equations of motion(HEOM) provide exact dynamics of open quantum systems coupled to harmonic baths, but their computational cost becomes prohibitive for systems with many independent local environments. In this work, we develop a symmetry-adapted HEOM formalism to significantly reduce the computational cost for the permutationally invariant Holstein-Tavis-Cummings (HTC) model. The method removes redundant information in two stages. First, all auxiliary density operators (ADOs) related only by relabeling identical molecules and their bath channels are replaced by a single canonical occupation-pattern representative. Second, molecules with the same local hierarchy occupation produce repeated matrix elements within each representative, allowing only the distinct complex variables to be propagated instead of the full (N + 1) $\times$ (N + 1) ADO matrices. The resulting matrix-free equations are evaluated using precomputed connections and molecular multiplicities. At fixed hierarchy depth L and number of bath correlation exponentials m, the number of canonical representatives becomes independent of the ensemble size for N $\geq$ L and the number of unique variables saturates for N $\geq$ L + 2. The formulation easily extends to multiple-exponential bath decompositions, arbitrary initial density operators, static disorders, and cavity loss. Our benchmarks reproduce conventional HEOM dynamics while requiring far fewer propagated variables and substantially less memory.
