Ovcharenko R, Fingerhut B P
Department of Chemistry and Centre for NanoScience, Ludwig-Maximilians-Universität München, 81377 München, Germany.
J Chem Phys. 2025 Jul 7;163(1). doi: 10.1063/5.0271212.
Path integral methods, such as the quasi-adiabatic propagator path integral (QUAPI), are widely used in general-purpose and highly accurate numerical benchmark simulations of open quantum systems, particularly in regimes inaccessible to perturbative methods. Nevertheless, the applicability of the QUAPI method to realistic systems of interest is restricted by the exponentially growing computer memory requirements with respect to the size of the quantum system and the time range of non-Markovian correlation effects. This exponential "wall" becomes even more severe for multiple non-commuting fluctuating environments. In the present work, we address the numerical efficiency and accuracy of approximations that have been introduced for the QUAPI method with a single general environment, for the case of two independent non-commuting environments where one of them is considered as a pure dephasing environment. In particular, we consider a sharply defined cutoff of the memory time, path filtering, and mask assisted coarse graining of influence functional coefficients as approximations. We demonstrate that commonly applied numerical techniques, such as path filtering, cannot be straightforwardly transferred to the two-bath case even in the weak-coupling and quasi-Markovian limits. On the other hand, the sharply defined memory cutoff can be accurately handled with the mask assisted coarse graining approach. Our findings demonstrate that if system coupling operators to different baths do not commute, the additive nature of the statistically independent environments may be misleading. In particular, the quasi-Markovian nature of a pure dephasing bath is lost once there simultaneously exists another non-commuting source of fluctuations.
路径积分方法，如准绝热传播子路径积分（QUAPI），广泛应用于开放量子系统的通用且高精度数值基准模拟中，特别是在微扰方法无法适用的情况下。然而，QUAPI方法在实际感兴趣的系统中的适用性受到计算机内存需求随量子系统大小和非马尔可夫关联效应时间范围呈指数增长的限制。对于多个非对易波动环境，这种指数“壁垒”变得更加严峻。在本工作中，我们针对具有单个一般环境的QUAPI方法所引入的近似的数值效率和准确性进行了研究，对于两个独立非对易环境的情况，其中一个被视为纯退相环境。特别地，我们将记忆时间的明确定义截断、路径滤波以及影响泛函系数的掩码辅助粗粒化作为近似方法进行考虑。我们证明，即使在弱耦合和准马尔可夫极限情况下，常用的数值技术，如路径滤波，也不能直接应用于双浴情况。另一方面，明确定义的记忆截断可以通过掩码辅助粗粒化方法精确处理。我们的研究结果表明，如果系统与不同浴的耦合算符不对易，统计独立环境的可加性可能会产生误导。特别是，一旦同时存在另一个非对易波动源，纯退相浴的准马尔可夫性质就会丧失。
