Hierarchical approach based on stochastic decoupling to dissipative systems

Based on the novel stochastic methodology for describing quantum dynamics of dissipative systems [J. Shao, J. Chem. Phys. 120 (2004) 5053], a hierarchical approach is suggested and applied to the spin–boson model with Debye spectral density function. The algorithm to implement this deterministic technique is expounded and the numerical results for the spin–boson system are explained.