Quantum dynamics of dissipative two-level systems and intradimer excitation energy transfer in the presence of static disorder

We use the numerically exact, fully quantum mechanical small matrix path integral (SMatPI) methodology to investigate the time evolution of the reduced density matrix (RDM) following photoexcitation of model molecular dimers in the presence or absence of static disorder. The dimer is modeled in terms of a two-level system that represents the excited electronic states of the monomers, which are coupled to a dissipative bath of vibrational modes with an Ohmic spectral density under diverse conditions that correspond to homo- or heterodimers, weak or moderately strong exciton-vibration coupling, high- or low-frequency vibrations, and high or low temperature. Through the equivalence class path integral algorithm, the averaging with respect to static disorder is performed with computational effort comparable to that of a single SMatPI calculation. We find that static disorder alters the dynamics and equilibrium properties of the RDM in significant and often subtle ways, which can mimic effects associated with stronger or weaker dissipation. The impact of disorder is most pronounced at low temperatures, where it tends to suppress coherence and often induces upward shifts in the population of the higher-lying state, while the effects on the off-diagonal RDM element and the eigenstate populations depend nonmonotonically on the asymmetry parameter. At high temperatures, the population shift is weaker and reversed for some parameters.