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We present a new, computationally inexpensive method for the calculation ofreduced density matrix dynamics for systems with a potentially large number ofsubsystem degrees of freedom coupled to a generic bath. The approach consistsof propagation of weak-coupling Redfield-like equations for the high frequencybath degrees of freedom only, while the low frequency bath modes aredynamically arrested but statistically sampled. We examine the improvementsafforded by this approximation by comparing with exact results for thespin-boson model over a wide range of parameter space. The results from themethod are found to dramatically improve Redfield dynamics in highlynon--Markovian regimes, at a similar computational cost. Relaxation of themode-freezing approximation via classical (Ehrenfest) evolution of the lowfrequency modes results in a dynamical hybrid method. We find that thisRedfield-based dynamical hybrid approach, which is computationally moreexpensive than bare Redfield dynamics, yields only a marginal improvement overthe simpler approximation of complete mode arrest.

Extending the applicability of Redfield theories into highly non-Markovian regimes