Advancing hierarchical equations of motion for efficient evaluation of coherent two-dimensional spectroscopy

To advance hierarchial equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg--Schrodinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focus on the effects of intermolecular transfer coupling and bi-exciton interaction.