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.

中文翻译：

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系统浴动力学的小矩阵路径积分。

通过递归地将纠缠的影响函数项递归分布在更长的时间间隔上，同​​时减小它们的大小，直到它们变为大小，才能获得路径积分表达式（SMatPI）的小矩阵分解，该分解产生与耗散谐波浴相互作用的系统的降低的密度矩阵。微不足道。这允许通过将尺寸等于裸系统的尺寸的小矩阵相乘来对路径积分变量进行逐一求和。分解的理论框架使用图解方法进行描述。分析和数值计算表明，时间纠缠变得可忽略的必要时间长度实际上与浴诱发的记忆相同。讨论了传播矩阵的性质和结构，