Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Hefei National Laboratory for Physical Sciences at the Microscale and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China.
J Chem Phys. 2018 Jun 21;148(23):234108. doi: 10.1063/1.5034776.
The hierarchical equations of motion (HEOM) theory is in principle exact for describing the dissipative dynamics of quantum systems linearly coupled to Gaussian environments. In practice, the hierarchy needs to be truncated at a finite tier. We demonstrate that, for general systems described by the fermionic HEOM, the (n+L̃)th-tier truncation with L̃=2NN yields the exact density operators up to the nth tier. Here, N = 2 for fermionic systems and N is the system degrees of freedom. For noninteracting systems, L̃ is further reduced by half. Such an exact termination pattern originates from the Pauli exclusion principle for fermions, and it holds true regardless of the system-environment coupling strength, the number of coupling reservoirs, or the specific scheme employed to unravel the environment memory contents. The relatively small L̃ emphasizes the nonperturbative nature of the HEOM theory. We also propose a simplified HEOM approach to further reduce the memory cost for practical calculations.
层次运动方程（HEOM）理论原则上可以精确描述与高斯环境线性耦合的量子系统的耗散动力学。在实践中，层次需要在有限的层次上截断。我们证明，对于由费米子 HEOM 描述的一般系统，（n+L̃）阶截断，其中 L̃=2NN，可得到精确的密度算符，最高可达 n 阶。这里，N=2 用于费米子系统，N 是系统自由度。对于非相互作用系统，L̃进一步减半。这种精确的终止模式源自费米子的泡利不相容原理，无论系统-环境耦合强度、耦合储层数量或用于揭示环境记忆内容的具体方案如何，它都成立。相对较小的 L̃强调了 HEOM 理论的非微扰性质。我们还提出了一种简化的 HEOM 方法，以进一步降低实际计算的内存成本。
