论文标题
基于树的小型矩阵路径积分的实现系统浴动力学不可或缺
Tree-based Implementation of the Small Matrix Path Integral for System-Bath Dynamics
论文作者
论文摘要
小矩阵路径积分（SMATPI）方法是一种有效的数值方法，用于模拟量子系统的演变与谐波浴的耦合。该方法依赖于一系列内核矩阵，该核矩阵定义了量子系统的非马克维亚动力学。在原始的SMATPI方法中，这些内核是通过QUAPI方法间接计算的。取而代之的是，我们专注于内核矩阵的定义，并揭示这些矩阵中的复发关系。使用这种关系，开发了基于树的算法（T-SMATPI），该算法比其定义基于其定义比对核矩阵的直接计算要快得多。该算法绕过了通过其他路径积分方法计算SMATPI矩阵的步骤，并提供了对SMATPI矩阵本身的更多了解。同时，它保持内存成本和计算成本较低。数值实验表明，T-SMATPI算法给出与I-Quapi和Smatpi完全相同的结果。尽管如此，我们的方法可能表明开放量子系统的一些新属性，并且有可能将其推广到高阶数值方案。
The small matrix path integral (SMatPI) method is an efficient numerical approach to simulate the evolution of a quantum system coupled to a harmonic bath. The method relies on a sequence of kernel matrices that defines the non-Markovian dynamics of the quantum system. In the original SMatPI method, these kernels are computed indirectly through the QuAPI method. Instead, we focus on the definition of the kernel matrices and reveal a recurrence relation in these matrices. Using such a relationship, a tree based algorithm (t-SMatPI) is developed, which is shown to be much faster than straightforward computation of the kernel matrices based on their definitions. This algorithm bypasses the step to compute the SMatPI matrices by other path integral methods and provides more understanding of the SMatPI matrices themselves. Meanwhile, it keeps the memory cost and computational cost low. Numerical experiments show that the t-SMatPI algorithm gives exactly the same result as i-QuAPI and SMatPI. In spite of this, our method may indicate some new properties of open quantum systems, and has the potential to be generalized to higher-order numerical schemes.
