Hierarchical dynamics of correlated system-environment coherence and optical spectroscopy.

We propose an efficient construction of the hierarchical equations of motion formalism of quantum dissipation on the basis of the Padé spectrum decomposition of the Bose function and the multiple brownian oscillators decomposition of the environment spectral density. The related hierarchical Liouville space algebra for quantum dissipative mechanics is outlined in relation to the evaluation of nonlinear optical response functions. With the simulated transient pump-probe spectroscopy of model exciton systems, we demonstrate the correlated system-environment coherence by the present nonperturbative and non-markovian quantum dissipation theory.