  Understanding coherent dynamics of excitons, spins, or hard-core bosons
(HCBs) has tremendous scientific and technological implications for light
harvesting and quantum computation. Here, we study decay of excited-state
population and decoherence in two models for HCBs, namely: an infinite-range
HCB model governed by Markovian dynamics and a two-site HCB model with
site-dependent strong potentials and subject to non-Markovian dynamics. Both
models are investigated in the regimes of antiadiabaticity and strong
HCB-phonon coupling with each site providing a different local optical phonon
environment; furthermore, the HCB systems in both models are taken to be
initially uncorrelated with the environment in the polaronic frame of
reference. For the infinite-range model, we derive an effective many-body
Hamiltonian that commutes with the long-range system Hamiltonian and thus has
the same set of eigenstates; consequently, a quantum-master-equation approach
shows that the quantum states of the system do not decohere. In the case of the
two-site HCB model, we show clearly that the degree of decoherence and decay of
excited state are enhanced by the proximity of the site-energy difference to
the eigenenergy of phonons and are most pronounced when the site-energy
difference is at resonance with twice the polaronic energy; additionally, the
decoherence and the decay effects are reduced when the strength of HCB-phonon
coupling is increased. Even for a multimode situation, the degree of
decoherence and decay are again dictated by the nearness of the energy
difference to the allowed phonon mode eigenenergies.
