A new method to account for the difference between classical and quantum baths in quantum dissipative dynamics

We investigate the difference between a quantum and classical bath within the Caldeira-Leggett model for dissipative quantum dynamics. It is well known that a Markovian equation of motion for the reduced dynamics can be derived by taking the classical approximation of the harmonic bath correlation function. However, such approximation is only valid at high temperatures, and it is necessary to include the non-Markovian effect of the quantum bath in more general cases. We show that the equation of motion derived for the classical bath can be extended to the exact quantum one, by simply adding a real stochastic process to take account of the difference between the quantum and classical bath correlation functions. Numerical examples in calculating electron and excitation energy transfer dynamics, as well as absorption spectra of molecular aggregates indicate that the proposed method is a valid approach to extend the existing theories to include the quantum effect of the harmonic bath. The possibility of applying a similar idea to account for the difference between zero and high temperature quantum dissipative dynamics is discussed.