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Unraveling the many facets of coherent and incoherent exciton motion in an ensemble of chromophores is an inherently complex quantum mechanical problem that has triggered a vivid debate on the role of quantum effects in molecular materials and biophysical systems. Here the dynamics of a statistical ensemble of molecular aggregates consisting of identical chromophores is investigated within a new theoretical framework. Taking account of intrinsic properties of the system, the Hamiltonian of the aggregate is partitioned into two mutually commuting vibrational and vibronic operators. This representation paves the way for an analysis that reveals the role of static disorder in ensembles of aggregates. Using analytical methods, it is demonstrated that after a critical time τ D ≃ 2π/σ (σ being the dispersion of the disorder) any dynamic variable of the aggregate exhibits purely vibrational dynamics. This result is confirmed by exact numerical calculations of the time-dependent site populations of the aggregate. These findings may be useful for the interpretation of recent femtosecond spectroscopic experiments on molecular aggregates.

Origin of Unexpectedly Simple Oscillatory Responses in the Excited-State Dynamics of Disordered Molecular Aggregates