AI 中文总结
本文提出一种精确约化算法，将TCL6生成器的计算复杂度从O(N_t^3)降至O(N_t log^2 N_t)，并推广至任意TCL阶，实现非马尔可夫开放量子系统的高效长时间模拟。
AI 中文摘要
在固定系统维度下，对所有$N_t$个采样时间点的Hadamard约化第六阶时间卷积无（TCL6）生成器进行直接求积需要$O(N_t^3)$次操作。我们针对一个通过一个厄米算符耦合到平稳中心高斯浴的有限维系统，推导出一个精确的约化方法。通过将固定的算符系数与标量浴核分离，完整的TCL6时间序列被约化为累积和与一阶递推、一维因果卷积，以及用于互锁历史的精确二进递归。利用该算法，在固定系统维度下，评估完整的TCL6时间序列需要$O(N_t\log^2 N_t)$次操作。此外，我们证明TCL$2n$可以以$O(N_t\log^{n-1} N_t)$的复杂度进行评估。浴关联函数的固定有限Matsubara展开允许在任何固定TCL阶数下以$O(N_t\log N_t)$进行评估。这些约化使得在TCL展开的有效范围内，能够快速进行非马尔可夫开放量子系统的长时间模拟。
英文摘要
Direct quadrature of the Hadamard-reduced sixth-order time-convolutionless (TCL6) generator at all $N_t$ sampled times requires $O(N_t^3)$ operations at fixed system dimension. We derive an exact reduction for a finite-dimensional system coupled through one Hermitian operator to a stationary centered Gaussian bath. By separating fixed operator coefficients from scalar bath kernels, the complete TCL6 time series is reduced to cumulative sums and first-order recurrences, one-dimensional causal convolutions, and an exact dyadic recursion for interlocked histories. With the algorithm, evaluating the complete TCL6 time series requires $O(N_t\log^2 N_t)$ operations at fixed system dimension. In addition, we show that TCL$2n$ can be evaluated with $O(N_t\log^{n-1} N_t)$ complexity. A fixed finite Matsubara expansion of the bath correlation function permits $O(N_t\log N_t)$ evaluation at any fixed TCL order. These reductions enable fast long-time simulations of non-Markovian open quantum systems within the regime of validity of the TCL expansion.
