The hierarchical equations of motion theory for Drude dissipation is optimized, with a convenient convergence criterion proposed in advance of numerical propagations. The theoretical construction is on basis of a Pad\'{e} spectrum decomposition that has been qualified to be the best sum-over-poles scheme for quantum distribution function. The resulting hierarchical dynamics under the {\em apriori} convergence criterion are exemplified with a benchmark spin-boson system, and also the transient absorption and two-dimensional spectroscopy of a model exciton dimer system.
@article{arxiv.1107.0249,
title = {Optimized hierarchical equations of motion for Drude dissipation},
author = {Jin-Jin Ding and Jian Xu and Jie Hu and Rui-Xue Xu and YiJing Yan},
journal= {arXiv preprint arXiv:1107.0249},
year = {2011}
}