Linearized approximations for condensed phase non-adiabatic dynamics: Multi-layered baths and Brownian dynamics implementation

Several approximate methods for propagating the density matrix of systems coupled to baths based on linearized approximations have been presented. Using influence functional formalism this approximation is explored in various limits for a condensed phase model. A new iterative stochastic propagation scheme is introduced that integrates out some of the bath degrees of freedom giving an effective evolution resembling Brownian dynamics. We show that this approach satisfies the fluctuation-dissipation theorem in various limits. The method is compared with alternative approximate full dimensional propagation schemes for the spin-boson model. The accuracy of the results is surprising since the scheme makes approximations about initialization at each iteration. This accuracy is encouraging since these kind of approaches hold significant potential computational saving for condensed phase quantum dynamics simulations as they give a systematic way of eliminating the explicit integration of a large number of environmental degrees of freedom.