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We study a series of $N$ oscillators each coupled to its nearest neighbours,and linearly to a phonon field through the oscillator's number operator. Weshow that the Hamiltonian of a pair of adjacent oscillators, or a dimer, withinthe series of oscillators can be transformed to a form in which they arecollectively coupled to the phonon field as a composite unit. In the weakcoupling and rotating-wave approximation, the system behaves effectively likethe trilinear boson model in the one excitation subspace of the dimersubsystem. The reduced dynamics of the one excitation subspace of the dimersubsystem coupled weakly to a phonon bath is similar to that of a two-levelsystem, with a metastable state against the vacuum. The decay constant of thesubsystem is proportional to the dephasing rate of the individual oscillator ina phonon bath, attenuated by a factor that depends on site asymmetry, intersitecoupling and the resonance frequency between the transformed oscillator modes,or excitons. As a result of the collective effect, the excitation relaxationlifetime is prolonged over the dephasing lifetime of an individual oscillatorcoupled to the same bath.

Attenuation of excitation decay rate due to collective effect