Fay Thomas P
Department of Chemistry, University of California, Berkeley, California 94720, USA.
J Chem Phys. 2022 Aug 7;157(5):054108. doi: 10.1063/5.0100365.
The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system-bath coupling strength. However, in its standard form, this method is only consistent with the weak-coupling quantum master equation at all temperatures when many auxiliary density operators are included in the hierarchy, even when low temperature corrections are included. Here, we propose a new low temperature correction scheme for the termination of the hierarchy based on Zwanzig projection, which alleviates this problem and restores consistency with the weak-coupling master equation with a minimal hierarchy. The utility of the new correction scheme is demonstrated on a range of model systems, including the Fenna-Matthews-Olson complex. The new closure is found to improve convergence of the HEOM even beyond the weak-coupling limit and is very straightforward to implement in existing HEOM codes.
开放系统量子动力学的研究因运动方程分层法（HEOM）而发生了变革，该方法能给出在任意温度和系统-浴耦合强度下与简谐振子浴耦合的系统的精确动力学。然而，在其标准形式下，即使包含低温修正，只有当分层中包含许多辅助密度算符时，此方法在所有温度下才与弱耦合量子主方程一致。在此，我们基于茨万齐格投影提出一种用于分层终止的新低温修正方案，该方案缓解了这一问题，并以最小的分层恢复了与弱耦合主方程的一致性。新修正方案的效用在一系列模型系统上得到了证明，包括芬纳-马修斯-奥尔森复合物。结果发现，新的封闭条件甚至在超出弱耦合极限的情况下也能改善HEOM的收敛性，并且在现有的HEOM代码中非常易于实现。
