Small Matrix Path Integral for System-Bath Dynamics.
Small Matrix Path Integral for System-Bath Dynamics.
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DOI：
10.1021/acs.jctc.0c00039
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发表时间：
2020-06
影响因子：
5.5
通讯作者：
N. Makri
中科院分区：
文献类型：
--
作者：
N. Makri
通过在较长时间内递归展开纠缠影响泛函项，同时减小它们的大小，直到这些项变得可以忽略，得到了路径积分表达式(SMatPI)的一个小矩阵分解，该分解得到了与耗散谐波槽相互作用的系统的约化密度矩阵。这允许通过将维度等于裸系统的维度的小矩阵相乘，在路径积分变量上逐个求和。用图解的方法描述了分解的理论框架。分析和数值计算表明，时间纠缠变得可以忽略所需的时间长度实际上与浴诱导记忆相同。讨论了传播子矩阵的性质和结构，并给出了在多态系统中的应用。
A small matrix decomposition of the path integral expression (SMatPI) that yields the reduced density matrix of a system interacting with a dissipative harmonic bath is obtained by recursively spreading the entangled influence functional terms over longer time intervals while simultaneously decreasing their magnitude until these terms become negligible. This allows summation over the path integral variables one by one through multiplication of small matrices with dimension equal to that of the bare system. The theoretical framework of the decomposition is described using a diagrammatic approach. Analytical and numerical calculations show that the necessary time length for the temporal entanglement to become negligible is practically the same as the bath-induced memory. The properties and structure of the propagator matrices are discussed, and applications to multistate systems are presented.