Hierarchical quantum master equation with semiclassical Drude dissipation.

We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation, which may be used with a great degree of confidence to various dynamics systems in condensed phases. The theoretical development is rooted in an improved semiclassical treatment of Drude bath, beyond the conventional high temperature approximations. It leads to the new theory a simple but important improvement over the conventional stochastic Liouville equation theory, without extra numerical cost. Its broad range of validity and applicability is extensively demonstrated with two-level electron transfer model systems, where the new theory can be considered as the modified Zusman equation. Criterion is also proposed to estimate the performance of the hierarchical quantum master equation.