Indirect communication between non-Markovian baths

In this work, we show that information transfer occurs between two baths, even in the absence of a direct coupling between the baths. This bath-system-bath-mediated information transfer leads to intricate non-Markovian dynamics in the open system considered. We show this through the development of a model for an undamped vibration in the presence of an overdamped bath. This two-bath model involves a new derivation of the hierarchical equations of motion (HEOM) for an overdamped Lorentz-Drude (LD) environment, which is combined with an undamped oscillator (UO) bath, termed LDUO-HEOM. The model is analyzed using expectation values of the bath coordinates, which demonstrates an approach to understanding dissipation and relaxation between multiple, coupled baths. The model generates 2D electronic spectra that are in qualitative agreement with single-bath models while eliminating additional superfluous damping, which was introduced by the finite spectral width of the underdamped bath in our previous two-bath underdamped-overdamped, "bath vibration model" [Humphries et al., J. Chem. Phys. 156, 084103 (2022)].