  We develop a quasiparticle approach to capture the dynamics of open quantum
systems coupled to bosonic thermal baths of arbitrary complexity based on the
Hierarchical Equations of Motion (HEOM). This is done by generalizing the HEOM
dynamics and mapping it into that of the system in interaction with a few
bosonic fictitious quasiparticles that we call bexcitons. Bexcitons arise from
a decomposition of the bath correlation function into discrete features.
Specifically, bexciton creation and annihilation couple the auxiliary density
matrices in the HEOM. The approach provides a systematic strategy to construct
exact quantum master equations that include the system-bath coupling to all
orders even for non-Markovian environments. Specifically, by introducing
different metrics and representations for the bexcitons it is possible to
straightforwardly generate different variants of the HEOM, demonstrating that
all these variants share a common underlying quasiparticle picture. Bexcitonic
properties, while unphysical, offer a coarse-grained view of the correlated
system-bath dynamics and its numerical convergence. For instance, we use it to
analyze the instability of the HEOM when the bath is composed of underdamped
oscillators and show that it leads to the creation of highly excited bexcitons.
The bexcitonic picture can also be used to develop more efficient approaches to
propagate the HEOM. As an example, we use the particle-like nature of the
bexcitons to introduce mode-combination of bexcitons that uses the
multi-configuration time-dependent Hartree to efficiently propagate the HEOM
dynamics.
