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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 the basis of a Padé spectrum decomposition that has been qualified to be the best sum-over-poles scheme for quantum distribution function. The resulting hierarchical dynamics under the a priori convergence criterion are exemplified with a benchmark spin-boson system, and also the transient absorption and related coherent two-dimensional spectroscopy of a model exciton dimer system. We combine the present theory with several advanced techniques such as the block hierarchical dynamics in mixed Heisenberg-Schrdinger picture and the on-the-fly filtering algorithm for the efficient evaluation of third-order optical response functions. © 2011 American Institute of Physics.

A nonperturbative quantum dissipation theory is developed based on an optimal construction of biexponential Drude bath correlation function for its influence on the system dynamics. It is an advanced hierarchical quantum master equation approach, aiming at a numerically efficient non-Markovian quantum dissipation propagator, with the support of a convenient criterion to estimate in advance its accuracy for general systems. Compared to its low level, single-exponential counterpart [R. X. Xu, J. Chem. Phys. 131, 214111 (2009)], the present theory remarkably improves the applicability range over all-parameter space, as tested critically with electron transfer and frequency-dispersed transient absorption of exciton dimer model systems. © 2010 American Institute of Physics.